TY  - JOUR
AU  - Jovanović, Predrag
AU  - Borka Jovanović, Vesna
AU  - Borka, Duško
AU  - Zakharov, Alexander F.
PY  - 2024
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/13024
AB  - Here we study possible improvements of the existing constraints on the upper bound of the graviton mass by the analysis of the stellar orbits around the supermassive black hole (SMBH) at the Galactic Center (GC) in the framework of Yukawa gravity. A motivation for this study is a recent detection of Schwarzschild precession in the orbit of S2 star around the SMBH at the GC by the GRAVITY Collaboration. The authors indicated that the orbital precession of the S2 star is close to the general relativity (GR) prediction, but with possible small deviation from it, and parametrized this effect by introducing an ad hoc factor in the parametrized post-Newtonian (PPN) equations of motion. Here we use the value of this factor presented by GRAVITY in order to perform two-body simulations of the stellar orbits in massive gravity using equations of motion in the modified PPN formalism, as well as to constrain the range of massive interaction Λ. From the obtained values of Λ, and assuming that it corresponds to the Compton wavelength of graviton, we then calculated new estimates for the upper bound of graviton mass which are found to be independent, but consistent with the LIGO’s estimate of graviton mass from the first gravitational wave (GW) signal GW150914 (later this graviton mass estimation was significantly improved with consequent observations of GW events). We also performed calculations including numerical simulations in order to constrain the bounds on graviton mass in the case of a small deviation of the stellar orbits from the corresponding GR predictions and showed that our method could further improve previous estimates for the upper bounds on the graviton mass. It is also demonstrated that such an analysis of the observed orbits of S-stars around the GC in the frame of the Yukawa gravity represents a tool for constraining the upper bound for the graviton mass, as well as for probing the predictions of GR or other gravity theories.
T2  - Physical Review D
T1  - Improvement of graviton mass constraints using GRAVITY’s detection of Schwarzschild precession in the orbit of S2 star around the Galactic Center
VL  - 109
IS  - 6
SP  - 064046
DO  - 10.1103/PhysRevD.109.064046
ER  - 

@article{
author = "Jovanović, Predrag and Borka Jovanović, Vesna and Borka, Duško and Zakharov, Alexander F.",
year = "2024",
abstract = "Here we study possible improvements of the existing constraints on the upper bound of the graviton mass by the analysis of the stellar orbits around the supermassive black hole (SMBH) at the Galactic Center (GC) in the framework of Yukawa gravity. A motivation for this study is a recent detection of Schwarzschild precession in the orbit of S2 star around the SMBH at the GC by the GRAVITY Collaboration. The authors indicated that the orbital precession of the S2 star is close to the general relativity (GR) prediction, but with possible small deviation from it, and parametrized this effect by introducing an ad hoc factor in the parametrized post-Newtonian (PPN) equations of motion. Here we use the value of this factor presented by GRAVITY in order to perform two-body simulations of the stellar orbits in massive gravity using equations of motion in the modified PPN formalism, as well as to constrain the range of massive interaction Λ. From the obtained values of Λ, and assuming that it corresponds to the Compton wavelength of graviton, we then calculated new estimates for the upper bound of graviton mass which are found to be independent, but consistent with the LIGO’s estimate of graviton mass from the first gravitational wave (GW) signal GW150914 (later this graviton mass estimation was significantly improved with consequent observations of GW events). We also performed calculations including numerical simulations in order to constrain the bounds on graviton mass in the case of a small deviation of the stellar orbits from the corresponding GR predictions and showed that our method could further improve previous estimates for the upper bounds on the graviton mass. It is also demonstrated that such an analysis of the observed orbits of S-stars around the GC in the frame of the Yukawa gravity represents a tool for constraining the upper bound for the graviton mass, as well as for probing the predictions of GR or other gravity theories.",
journal = "Physical Review D",
title = "Improvement of graviton mass constraints using GRAVITY’s detection of Schwarzschild precession in the orbit of S2 star around the Galactic Center",
volume = "109",
number = "6",
pages = "064046",
doi = "10.1103/PhysRevD.109.064046"
}

Jovanović, P., Borka Jovanović, V., Borka, D.,& Zakharov, A. F.. (2024). Improvement of graviton mass constraints using GRAVITY’s detection of Schwarzschild precession in the orbit of S2 star around the Galactic Center. in Physical Review D, 109(6), 064046.
https://doi.org/10.1103/PhysRevD.109.064046

Jovanović P, Borka Jovanović V, Borka D, Zakharov AF. Improvement of graviton mass constraints using GRAVITY’s detection of Schwarzschild precession in the orbit of S2 star around the Galactic Center. in Physical Review D. 2024;109(6):064046.
doi:10.1103/PhysRevD.109.064046 .

Jovanović, Predrag, Borka Jovanović, Vesna, Borka, Duško, Zakharov, Alexander F., "Improvement of graviton mass constraints using GRAVITY’s detection of Schwarzschild precession in the orbit of S2 star around the Galactic Center" in Physical Review D, 109, no. 6 (2024):064046,
https://doi.org/10.1103/PhysRevD.109.064046 . .

TY  - JOUR
AU  - Jovanović, Predrag
AU  - Borka Jovanović, Vesna
AU  - Borka, Duško
AU  - Zakharov, Alexander F.
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10849
AB  - In this paper we investigate a Yukawa gravity modification of the Newtonian gravitational potential in a weak field approximation. For that purpose we derived the corresponding equations of motion and used them to perform two-body simulations of the stellar orbits. In 2020 the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center (GC) and showed that it is close to the general relativity (GR) prediction. Using this observational fact, we evaluated parameters of the Yukawa gravity (the range of Yukawa interaction Λ and universal constant δ) with the Schwarzschild precession of the S-stars assuming that the observed values as indicated by the GRAVITY Collaboration will have a small deviation from GR prediction [1]. GR provides the most natural way to fit observational data for S-star orbits, however, their precessions can be fitted by Yukawa gravity. Our main goal was to study the possible influence of the strength of Yukawa interaction, i.e. the universal constant δ, on the precessions of S-star orbits. We analyze S-star orbits assuming different strength of Yukawa interaction δ and find that this parameter has strong influence on range of Yukawa interaction Λ. For that purpose we use parameterized post-Newtonian (PPN) equations of motion in order to calculate the simulated orbits of S-stars in GR and Yukawa gravity. Using MCMC simulations we obtain the best-fit values and uncertainties of Yukawa gravity parameters for S-stars. Also, we introduce a new criterion which can be used for classification of gravitational systems in this type of gravity, according to their scales. We demonstrated that performed analysis of the observed S-stars orbits around the GC in the frame of the Yukawa gravity represent a tool for constraining the Yukawa gravity parameters and probing the predictions of gravity theories.
T2  - Journal of Cosmology and Astroparticle Physics
T1  - Constraints on Yukawa gravity parameters from observations of bright stars
IS  - 03
SP  - 056
DO  - 10.1088/1475-7516/2023/03/056
ER  - 

@article{
author = "Jovanović, Predrag and Borka Jovanović, Vesna and Borka, Duško and Zakharov, Alexander F.",
year = "2023",
abstract = "In this paper we investigate a Yukawa gravity modification of the Newtonian gravitational potential in a weak field approximation. For that purpose we derived the corresponding equations of motion and used them to perform two-body simulations of the stellar orbits. In 2020 the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center (GC) and showed that it is close to the general relativity (GR) prediction. Using this observational fact, we evaluated parameters of the Yukawa gravity (the range of Yukawa interaction Λ and universal constant δ) with the Schwarzschild precession of the S-stars assuming that the observed values as indicated by the GRAVITY Collaboration will have a small deviation from GR prediction [1]. GR provides the most natural way to fit observational data for S-star orbits, however, their precessions can be fitted by Yukawa gravity. Our main goal was to study the possible influence of the strength of Yukawa interaction, i.e. the universal constant δ, on the precessions of S-star orbits. We analyze S-star orbits assuming different strength of Yukawa interaction δ and find that this parameter has strong influence on range of Yukawa interaction Λ. For that purpose we use parameterized post-Newtonian (PPN) equations of motion in order to calculate the simulated orbits of S-stars in GR and Yukawa gravity. Using MCMC simulations we obtain the best-fit values and uncertainties of Yukawa gravity parameters for S-stars. Also, we introduce a new criterion which can be used for classification of gravitational systems in this type of gravity, according to their scales. We demonstrated that performed analysis of the observed S-stars orbits around the GC in the frame of the Yukawa gravity represent a tool for constraining the Yukawa gravity parameters and probing the predictions of gravity theories.",
journal = "Journal of Cosmology and Astroparticle Physics",
title = "Constraints on Yukawa gravity parameters from observations of bright stars",
number = "03",
pages = "056",
doi = "10.1088/1475-7516/2023/03/056"
}

Jovanović, P., Borka Jovanović, V., Borka, D.,& Zakharov, A. F.. (2023). Constraints on Yukawa gravity parameters from observations of bright stars. in Journal of Cosmology and Astroparticle Physics(03), 056.
https://doi.org/10.1088/1475-7516/2023/03/056

Jovanović P, Borka Jovanović V, Borka D, Zakharov AF. Constraints on Yukawa gravity parameters from observations of bright stars. in Journal of Cosmology and Astroparticle Physics. 2023;(03):056.
doi:10.1088/1475-7516/2023/03/056 .

Jovanović, Predrag, Borka Jovanović, Vesna, Borka, Duško, Zakharov, Alexander F., "Constraints on Yukawa gravity parameters from observations of bright stars" in Journal of Cosmology and Astroparticle Physics, no. 03 (2023):056,
https://doi.org/10.1088/1475-7516/2023/03/056 . .

TY  - JOUR
AU  - Borka, Duško
AU  - Borka Jovanović, Vesna
AU  - Capozziello, Salvatore
AU  - Zakharov, Alexander F.
AU  - Jovanović, Predrag
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9981
AB  - After giving a short overview of previous results on constraining of Extended Gravity by stellar orbits, we discuss the Schwarzschild orbital precession of S2 star assuming the congruence with predictions of General Relativity (GR). At the moment, the S2 star trajectory is remarkably fitted with the first post-Newtonian approximation of GR. In particular, both Keck and VLT (GRAVITY) teams declared that the gravitational redshift near its pericenter passage for the S2 star orbit corresponds to theoretical estimates found with the first post-Newtonian (pN) approximation. In 2020, the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center and showed that it is close to the GR prediction. Based on this observational fact, we evaluated parameters of the Extended Gravity theories with the Schwarzschild precession of the S2 star. Using the mentioned method, we estimate the orbital precession angles for some Extended Gravity models including power-law f(R), general Yukawa-like corrections, scalar–tensor gravity, and non-local gravity theories formulated in both metric and Palatini formalism. In this consideration, we assume that a gravitational field is spherically symmetric, therefore, alternative theories of gravity could be described only with a few parameters. Specifically, considering the orbital precession, we estimate the range of parameters of these Extended Gravity models for which the orbital precession is like in GR. Then we compare these results with our previous results, which were obtained by fitting the simulated orbits of S2 star to its observed astrometric positions. In case of power-law f(R), generic Yukawa-like correction, scalar–tensor gravity and non-local gravity theories, we were able to obtain a prograde orbital precession, like in GR. According to these results, the method is a useful tool to evaluate parameters of the gravitational potential at the Galactic Center.
T2  - Universe
T1  - Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star
VL  - 7
IS  - 11
SP  - 407
DO  - 10.3390/universe7110407
ER  - 

@article{
author = "Borka, Duško and Borka Jovanović, Vesna and Capozziello, Salvatore and Zakharov, Alexander F. and Jovanović, Predrag",
year = "2021",
abstract = "After giving a short overview of previous results on constraining of Extended Gravity by stellar orbits, we discuss the Schwarzschild orbital precession of S2 star assuming the congruence with predictions of General Relativity (GR). At the moment, the S2 star trajectory is remarkably fitted with the first post-Newtonian approximation of GR. In particular, both Keck and VLT (GRAVITY) teams declared that the gravitational redshift near its pericenter passage for the S2 star orbit corresponds to theoretical estimates found with the first post-Newtonian (pN) approximation. In 2020, the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center and showed that it is close to the GR prediction. Based on this observational fact, we evaluated parameters of the Extended Gravity theories with the Schwarzschild precession of the S2 star. Using the mentioned method, we estimate the orbital precession angles for some Extended Gravity models including power-law f(R), general Yukawa-like corrections, scalar–tensor gravity, and non-local gravity theories formulated in both metric and Palatini formalism. In this consideration, we assume that a gravitational field is spherically symmetric, therefore, alternative theories of gravity could be described only with a few parameters. Specifically, considering the orbital precession, we estimate the range of parameters of these Extended Gravity models for which the orbital precession is like in GR. Then we compare these results with our previous results, which were obtained by fitting the simulated orbits of S2 star to its observed astrometric positions. In case of power-law f(R), generic Yukawa-like correction, scalar–tensor gravity and non-local gravity theories, we were able to obtain a prograde orbital precession, like in GR. According to these results, the method is a useful tool to evaluate parameters of the gravitational potential at the Galactic Center.",
journal = "Universe",
title = "Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star",
volume = "7",
number = "11",
pages = "407",
doi = "10.3390/universe7110407"
}

Borka, D., Borka Jovanović, V., Capozziello, S., Zakharov, A. F.,& Jovanović, P.. (2021). Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star. in Universe, 7(11), 407.
https://doi.org/10.3390/universe7110407

Borka D, Borka Jovanović V, Capozziello S, Zakharov AF, Jovanović P. Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star. in Universe. 2021;7(11):407.
doi:10.3390/universe7110407 .

Borka, Duško, Borka Jovanović, Vesna, Capozziello, Salvatore, Zakharov, Alexander F., Jovanović, Predrag, "Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star" in Universe, 7, no. 11 (2021):407,
https://doi.org/10.3390/universe7110407 . .

TY  - JOUR
AU  - Zakharov, Alexander F.
AU  - Jovanović, Predrag
AU  - Borka, Duško
AU  - Borka Jovanović, Vesna
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8826
AB  - It is established that there are supermassive black holes in centers of galaxies. A supermassive black hole with mass around 4 × 106 M⊙ is located at the Galactic Center. Such an approach for the Galactic Center looks rather natural, in spite of that consequences of model must be checked with observa- tions. We discuss opportunities to check this with forthcoming observations of shadows in mm band for the Galactic Center as it was done recently for M87*. Observations of bright stars moving near the Galactic Center gives another op-portunity to evaluate gravitational potential. We discuss opportunities to use these observations to constrain alternative theories of gravity. © 2020, Astronomical Institute, Slovak Academy of Sciences.
T2  - Contributions of the Astronomical Observatory Skalnaté Pleso
T1  - Observational tests of general relativity and alternative theories of gravity with Galactic Center observations using current and future large observational facilities
VL  - 50
IS  - 1
SP  - 203
EP  - 218
DO  - 10.31577/caosp.2020.50.1.203
ER  - 

@article{
author = "Zakharov, Alexander F. and Jovanović, Predrag and Borka, Duško and Borka Jovanović, Vesna",
year = "2020",
abstract = "It is established that there are supermassive black holes in centers of galaxies. A supermassive black hole with mass around 4 × 106 M⊙ is located at the Galactic Center. Such an approach for the Galactic Center looks rather natural, in spite of that consequences of model must be checked with observa- tions. We discuss opportunities to check this with forthcoming observations of shadows in mm band for the Galactic Center as it was done recently for M87*. Observations of bright stars moving near the Galactic Center gives another op-portunity to evaluate gravitational potential. We discuss opportunities to use these observations to constrain alternative theories of gravity. © 2020, Astronomical Institute, Slovak Academy of Sciences.",
journal = "Contributions of the Astronomical Observatory Skalnaté Pleso",
title = "Observational tests of general relativity and alternative theories of gravity with Galactic Center observations using current and future large observational facilities",
volume = "50",
number = "1",
pages = "203-218",
doi = "10.31577/caosp.2020.50.1.203"
}

Zakharov, A. F., Jovanović, P., Borka, D.,& Borka Jovanović, V.. (2020). Observational tests of general relativity and alternative theories of gravity with Galactic Center observations using current and future large observational facilities. in Contributions of the Astronomical Observatory Skalnaté Pleso, 50(1), 203-218.
https://doi.org/10.31577/caosp.2020.50.1.203

Zakharov AF, Jovanović P, Borka D, Borka Jovanović V. Observational tests of general relativity and alternative theories of gravity with Galactic Center observations using current and future large observational facilities. in Contributions of the Astronomical Observatory Skalnaté Pleso. 2020;50(1):203-218.
doi:10.31577/caosp.2020.50.1.203 .

Zakharov, Alexander F., Jovanović, Predrag, Borka, Duško, Borka Jovanović, Vesna, "Observational tests of general relativity and alternative theories of gravity with Galactic Center observations using current and future large observational facilities" in Contributions of the Astronomical Observatory Skalnaté Pleso, 50, no. 1 (2020):203-218,
https://doi.org/10.31577/caosp.2020.50.1.203 . .

TY  - JOUR
AU  - Zakharov, Alexander F.
AU  - Jovanović, Predrag
AU  - Borka, Duško
AU  - Borka Jovanović, Vesna
PY  - 2018
UR  - http://stacks.iop.org/1475-7516/2018/i=04/a=050?key=crossref.a23e3c8d44b40fe0c07114ff29f9d9ae
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7668
AB  - Recently, the LIGO-Virgo collaboration discovered gravitational waves and in their first publication on the subject the authors also presented a graviton mass constraint as m(g) < 1.2 x 10(-22) eV {[}1] (see also more details in a complimentary paper {[}2]). In our previous papers we considered constraints on Yukawa gravity parameters {[}3] and on graviton mass from analysis of the trajectory of S2 star near the Galactic Center {[}4]. In the paper we analyze a potential to reduce upper bounds for graviton mass with future observational data on trajectories of bright stars near the Galactic Center. Since gravitational potentials are different for these two cases, expressions for relativistic advance for general relativity and Yukawa potential are different functions on eccentricity and semimajor axis, it gives an opportunity to improve current estimates of graviton mass with future observational facilities. In our considerations of an improvement potential for a graviton mass estimate we adopt a conservative strategy and assume that trajectories of bright stars and their apocenter advance will be described with general relativity expressions and it gives opportunities to improve graviton mass constraints. In contrast with our previous studies, where we present current constraints on parameters of Yukawa gravity {[}3] and graviton mass {[}4] from observations of S2 star, in the paper we express expectations to improve current constraints for graviton mass, assuming the GR predictions about apocenter shifts will be confirmed with future observations. We concluded that if future observations of bright star orbits during around fifty years will confirm GR predictions about apocenter shifts of bright star orbits it give an opportunity to constrain a graviton mass at a level around 5 x 10(-23) eV or slightly better than current estimates obtained with LIGO observations.
T2  - Journal of Cosmology and Astroparticle Physics
T1  - Constraining the range of Yukawa gravity interaction from S2 star orbits III: improvement expectations for graviton mass bounds
VL  - 2018
IS  - 04
SP  - 050
EP  - 050
DO  - 10.1088/1475-7516/2018/04/050
ER  - 

@article{
author = "Zakharov, Alexander F. and Jovanović, Predrag and Borka, Duško and Borka Jovanović, Vesna",
year = "2018",
abstract = "Recently, the LIGO-Virgo collaboration discovered gravitational waves and in their first publication on the subject the authors also presented a graviton mass constraint as m(g) < 1.2 x 10(-22) eV {[}1] (see also more details in a complimentary paper {[}2]). In our previous papers we considered constraints on Yukawa gravity parameters {[}3] and on graviton mass from analysis of the trajectory of S2 star near the Galactic Center {[}4]. In the paper we analyze a potential to reduce upper bounds for graviton mass with future observational data on trajectories of bright stars near the Galactic Center. Since gravitational potentials are different for these two cases, expressions for relativistic advance for general relativity and Yukawa potential are different functions on eccentricity and semimajor axis, it gives an opportunity to improve current estimates of graviton mass with future observational facilities. In our considerations of an improvement potential for a graviton mass estimate we adopt a conservative strategy and assume that trajectories of bright stars and their apocenter advance will be described with general relativity expressions and it gives opportunities to improve graviton mass constraints. In contrast with our previous studies, where we present current constraints on parameters of Yukawa gravity {[}3] and graviton mass {[}4] from observations of S2 star, in the paper we express expectations to improve current constraints for graviton mass, assuming the GR predictions about apocenter shifts will be confirmed with future observations. We concluded that if future observations of bright star orbits during around fifty years will confirm GR predictions about apocenter shifts of bright star orbits it give an opportunity to constrain a graviton mass at a level around 5 x 10(-23) eV or slightly better than current estimates obtained with LIGO observations.",
journal = "Journal of Cosmology and Astroparticle Physics",
title = "Constraining the range of Yukawa gravity interaction from S2 star orbits III: improvement expectations for graviton mass bounds",
volume = "2018",
number = "04",
pages = "050-050",
doi = "10.1088/1475-7516/2018/04/050"
}

Zakharov, A. F., Jovanović, P., Borka, D.,& Borka Jovanović, V.. (2018). Constraining the range of Yukawa gravity interaction from S2 star orbits III: improvement expectations for graviton mass bounds. in Journal of Cosmology and Astroparticle Physics, 2018(04), 050-050.
https://doi.org/10.1088/1475-7516/2018/04/050

Zakharov AF, Jovanović P, Borka D, Borka Jovanović V. Constraining the range of Yukawa gravity interaction from S2 star orbits III: improvement expectations for graviton mass bounds. in Journal of Cosmology and Astroparticle Physics. 2018;2018(04):050-050.
doi:10.1088/1475-7516/2018/04/050 .

Zakharov, Alexander F., Jovanović, Predrag, Borka, Duško, Borka Jovanović, Vesna, "Constraining the range of Yukawa gravity interaction from S2 star orbits III: improvement expectations for graviton mass bounds" in Journal of Cosmology and Astroparticle Physics, 2018, no. 04 (2018):050-050,
https://doi.org/10.1088/1475-7516/2018/04/050 . .

TY  - CONF
AU  - Zakharov, Alexander F.
AU  - Jovanović, Predrag
AU  - Borka, Duško
AU  - Borka Jovanović, Vesna
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7166
AB  - One could use trajectories of test particles to evaluate a gravitational potential. In particular, in the case of the Galactic Center one could use photon trajectories to analyze a shadow structure. Another way is to use bright stars near the Galactic Center to evaluate a gravitational potential and constrain parameters of a model for the Galactic Center. In particular, one could obtain constraints on parameters of black hole, stellar cluster and dark matter concentration. Earlier, we constrained parameters of Fr and a Yukawa potential from observational data for the S2 star trajectory. Now gravity theories with a massive graviton are a subject of intensive studies. People proposed different experimental ways to evaluate a graviton mass. Recently, the joint LIGO and VIRGO collaboration reported not only a discovery of gravitational waves and binary black holes, but the team claimed also that found a constraint on a graviton mass as 1.2 x 10(-22) eV. We show that an analysis of the S2 star trajectory could constrain a graviton mass with a comparable accuracy and this constraint is consistent with LIGOs one.
C3  - Journal of Physics: Conference Series
T1  - Graviton mass evaluation with trajectories of bright stars at the Galactic Center
VL  - 798
DO  - 10.1088/1742-6596/798/1/012081
ER  - 

@conference{
author = "Zakharov, Alexander F. and Jovanović, Predrag and Borka, Duško and Borka Jovanović, Vesna",
year = "2017",
abstract = "One could use trajectories of test particles to evaluate a gravitational potential. In particular, in the case of the Galactic Center one could use photon trajectories to analyze a shadow structure. Another way is to use bright stars near the Galactic Center to evaluate a gravitational potential and constrain parameters of a model for the Galactic Center. In particular, one could obtain constraints on parameters of black hole, stellar cluster and dark matter concentration. Earlier, we constrained parameters of Fr and a Yukawa potential from observational data for the S2 star trajectory. Now gravity theories with a massive graviton are a subject of intensive studies. People proposed different experimental ways to evaluate a graviton mass. Recently, the joint LIGO and VIRGO collaboration reported not only a discovery of gravitational waves and binary black holes, but the team claimed also that found a constraint on a graviton mass as 1.2 x 10(-22) eV. We show that an analysis of the S2 star trajectory could constrain a graviton mass with a comparable accuracy and this constraint is consistent with LIGOs one.",
journal = "Journal of Physics: Conference Series",
title = "Graviton mass evaluation with trajectories of bright stars at the Galactic Center",
volume = "798",
doi = "10.1088/1742-6596/798/1/012081"
}

Zakharov, A. F., Jovanović, P., Borka, D.,& Borka Jovanović, V.. (2017). Graviton mass evaluation with trajectories of bright stars at the Galactic Center. in Journal of Physics: Conference Series, 798.
https://doi.org/10.1088/1742-6596/798/1/012081

Zakharov AF, Jovanović P, Borka D, Borka Jovanović V. Graviton mass evaluation with trajectories of bright stars at the Galactic Center. in Journal of Physics: Conference Series. 2017;798.
doi:10.1088/1742-6596/798/1/012081 .

Zakharov, Alexander F., Jovanović, Predrag, Borka, Duško, Borka Jovanović, Vesna, "Graviton mass evaluation with trajectories of bright stars at the Galactic Center" in Journal of Physics: Conference Series, 798 (2017),
https://doi.org/10.1088/1742-6596/798/1/012081 . .

TY  - CONF
AU  - Zakharov, Alexander F.
AU  - Jovanović, Predrag
AU  - Borka, Duško
AU  - Borka Jovanović, Vesna
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7172
AB  - In February 2016 the LIGO and VIRGO collaboration reported the discovery of gravitational waves in merging black holes, therefore, the team confirmed GR predictions about an existence of black holes and gravitational waves in the strong gravitational field limit. Moreover, in their papers the joint LIGO and VIRGO team presented an upper limit on graviton mass such as m(g) LT 1.2 x 10(-22) eV (Abbott et al. 2016). So, the authors concluded that their observational data do not show any violation of classical general relativity. We show that an analysis of bright star trajectories could constrain graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and the estimate is consistent with the one obtained by the LIGO and VIRGO collaboration. This analysis gives an opportunity to treat observations of bright stars near the Galactic Center as a useful tool to obtain constraints on the fundamental gravity law such as modifications of the Newton gravity law in a weak field approximation. In that way, based on a potential reconstruction at the Galactic Center we obtain bounds on a graviton mass.
C3  - EPJ Web of Conferences
T1  - Graviton mass bounds from an analysis of bright star trajectories at the Galactic Center
VL  - 138
SP  - UNSP 01010
DO  - 10.1051/epjconf/201713801010
ER  - 

@conference{
author = "Zakharov, Alexander F. and Jovanović, Predrag and Borka, Duško and Borka Jovanović, Vesna",
year = "2017",
abstract = "In February 2016 the LIGO and VIRGO collaboration reported the discovery of gravitational waves in merging black holes, therefore, the team confirmed GR predictions about an existence of black holes and gravitational waves in the strong gravitational field limit. Moreover, in their papers the joint LIGO and VIRGO team presented an upper limit on graviton mass such as m(g) LT 1.2 x 10(-22) eV (Abbott et al. 2016). So, the authors concluded that their observational data do not show any violation of classical general relativity. We show that an analysis of bright star trajectories could constrain graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and the estimate is consistent with the one obtained by the LIGO and VIRGO collaboration. This analysis gives an opportunity to treat observations of bright stars near the Galactic Center as a useful tool to obtain constraints on the fundamental gravity law such as modifications of the Newton gravity law in a weak field approximation. In that way, based on a potential reconstruction at the Galactic Center we obtain bounds on a graviton mass.",
journal = "EPJ Web of Conferences",
title = "Graviton mass bounds from an analysis of bright star trajectories at the Galactic Center",
volume = "138",
pages = "UNSP 01010",
doi = "10.1051/epjconf/201713801010"
}

Zakharov, A. F., Jovanović, P., Borka, D.,& Borka Jovanović, V.. (2017). Graviton mass bounds from an analysis of bright star trajectories at the Galactic Center. in EPJ Web of Conferences, 138, UNSP 01010.
https://doi.org/10.1051/epjconf/201713801010

Zakharov AF, Jovanović P, Borka D, Borka Jovanović V. Graviton mass bounds from an analysis of bright star trajectories at the Galactic Center. in EPJ Web of Conferences. 2017;138:UNSP 01010.
doi:10.1051/epjconf/201713801010 .

Zakharov, Alexander F., Jovanović, Predrag, Borka, Duško, Borka Jovanović, Vesna, "Graviton mass bounds from an analysis of bright star trajectories at the Galactic Center" in EPJ Web of Conferences, 138 (2017):UNSP 01010,
https://doi.org/10.1051/epjconf/201713801010 . .

TY  - CONF
AU  - Zakharov, Alexander F.
AU  - Jovanović, Predrag
AU  - Borka, Duško
AU  - Borka Jovanović, Vesna
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7119
AB  - Scientists worked in Saint-Petersburg (Petrograd, Leningrad) played the extremely important role in creation of scientific school and development of general relativity in Russia. Very recently LIGO collaboration discovered gravitational waves [1] predicted 100 years ago by A. Einstein. In the papers reporting about this discovery, the joint LIGO and VIRGO team presented an upper limit on graviton mass such as m(g) LT 1.2 x 10(-22) eV [1, 2]. The authors concluded that their observational data do not show violations of classical general relativity because the graviton mass limit is very small. We show that an analysis of bright star trajectories could bound graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and expected with forthcoming pulsar timing observations for gravitational wave detection. This analysis gives an opportunity to treat observations of bright stars near the Galactic Center as a tool for an evaluation specific parameters of the black hole and also to obtain constraints on the fundamental gravity law such as a modifications of Newton gravity law in a weak field approximation. In that way, based on a potential reconstruction at the Galactic Center we give a bounds on a graviton mass.
C3  - EPJ Web of Conferences
T1  - Trajectories of bright stars at the Galactic Center as a tool to evaluate a graviton mass
VL  - 125
DO  - 10.1051/epjconf/201612501011
ER  - 

@conference{
author = "Zakharov, Alexander F. and Jovanović, Predrag and Borka, Duško and Borka Jovanović, Vesna",
year = "2016",
abstract = "Scientists worked in Saint-Petersburg (Petrograd, Leningrad) played the extremely important role in creation of scientific school and development of general relativity in Russia. Very recently LIGO collaboration discovered gravitational waves [1] predicted 100 years ago by A. Einstein. In the papers reporting about this discovery, the joint LIGO and VIRGO team presented an upper limit on graviton mass such as m(g) LT 1.2 x 10(-22) eV [1, 2]. The authors concluded that their observational data do not show violations of classical general relativity because the graviton mass limit is very small. We show that an analysis of bright star trajectories could bound graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and expected with forthcoming pulsar timing observations for gravitational wave detection. This analysis gives an opportunity to treat observations of bright stars near the Galactic Center as a tool for an evaluation specific parameters of the black hole and also to obtain constraints on the fundamental gravity law such as a modifications of Newton gravity law in a weak field approximation. In that way, based on a potential reconstruction at the Galactic Center we give a bounds on a graviton mass.",
journal = "EPJ Web of Conferences",
title = "Trajectories of bright stars at the Galactic Center as a tool to evaluate a graviton mass",
volume = "125",
doi = "10.1051/epjconf/201612501011"
}

Zakharov, A. F., Jovanović, P., Borka, D.,& Borka Jovanović, V.. (2016). Trajectories of bright stars at the Galactic Center as a tool to evaluate a graviton mass. in EPJ Web of Conferences, 125.
https://doi.org/10.1051/epjconf/201612501011

Zakharov AF, Jovanović P, Borka D, Borka Jovanović V. Trajectories of bright stars at the Galactic Center as a tool to evaluate a graviton mass. in EPJ Web of Conferences. 2016;125.
doi:10.1051/epjconf/201612501011 .

Zakharov, Alexander F., Jovanović, Predrag, Borka, Duško, Borka Jovanović, Vesna, "Trajectories of bright stars at the Galactic Center as a tool to evaluate a graviton mass" in EPJ Web of Conferences, 125 (2016),
https://doi.org/10.1051/epjconf/201612501011 . .

TY  - JOUR
AU  - Zakharov, Alexander F.
AU  - Jovanović, Predrag
AU  - Borka, Duško
AU  - Borka Jovanović, Vesna
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1125
AB  - Recently LIGO collaboration discovered gravitational waves [1] predicted 100 years ago by A. Einstein. Moreover, in the key paper reporting about the discovery, the joint LIGO and VIRGO team presented an upper limit on graviton mass such as m(g) LT 1.2 x 10(-22)eV [1] (see also more details in another LIGO paper [2] dedicated to a data analysis to obtain such a small constraint on a graviton mass). Since the graviton mass limit is so small the authors concluded that their observational data do not show violations of classical general relativity. We consider another opportunity to evaluate a graviton mass from phenomenological consequences of massive gravity and show that an analysis of bright star trajectories could bound graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and expected with forthcoming pulsar timing observations for gravitational wave detection. It gives an opportunity to treat observations of bright stars near the Galactic Center as a wonderful tool not only for an evaluation specific parameters of the black hole but also to obtain constraints on the fundamental gravity law such as a modifications of Newton gravity law in a weak field approximation. In particular, we obtain bounds on a graviton mass based on a potential reconstruction at the Galactic Center.
T2  - Journal of Cosmology and Astroparticle Physics
T1  - Constraining the range of Yukawa gravity interaction from S2 star orbits II: bounds on graviton mass
IS  - 5
DO  - 10.1088/1475-7516/2016/05/045
ER  - 

@article{
author = "Zakharov, Alexander F. and Jovanović, Predrag and Borka, Duško and Borka Jovanović, Vesna",
year = "2016",
abstract = "Recently LIGO collaboration discovered gravitational waves [1] predicted 100 years ago by A. Einstein. Moreover, in the key paper reporting about the discovery, the joint LIGO and VIRGO team presented an upper limit on graviton mass such as m(g) LT 1.2 x 10(-22)eV [1] (see also more details in another LIGO paper [2] dedicated to a data analysis to obtain such a small constraint on a graviton mass). Since the graviton mass limit is so small the authors concluded that their observational data do not show violations of classical general relativity. We consider another opportunity to evaluate a graviton mass from phenomenological consequences of massive gravity and show that an analysis of bright star trajectories could bound graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and expected with forthcoming pulsar timing observations for gravitational wave detection. It gives an opportunity to treat observations of bright stars near the Galactic Center as a wonderful tool not only for an evaluation specific parameters of the black hole but also to obtain constraints on the fundamental gravity law such as a modifications of Newton gravity law in a weak field approximation. In particular, we obtain bounds on a graviton mass based on a potential reconstruction at the Galactic Center.",
journal = "Journal of Cosmology and Astroparticle Physics",
title = "Constraining the range of Yukawa gravity interaction from S2 star orbits II: bounds on graviton mass",
number = "5",
doi = "10.1088/1475-7516/2016/05/045"
}

Zakharov, A. F., Jovanović, P., Borka, D.,& Borka Jovanović, V.. (2016). Constraining the range of Yukawa gravity interaction from S2 star orbits II: bounds on graviton mass. in Journal of Cosmology and Astroparticle Physics(5).
https://doi.org/10.1088/1475-7516/2016/05/045

Zakharov AF, Jovanović P, Borka D, Borka Jovanović V. Constraining the range of Yukawa gravity interaction from S2 star orbits II: bounds on graviton mass. in Journal of Cosmology and Astroparticle Physics. 2016;(5).
doi:10.1088/1475-7516/2016/05/045 .

Zakharov, Alexander F., Jovanović, Predrag, Borka, Duško, Borka Jovanović, Vesna, "Constraining the range of Yukawa gravity interaction from S2 star orbits II: bounds on graviton mass" in Journal of Cosmology and Astroparticle Physics, no. 5 (2016),
https://doi.org/10.1088/1475-7516/2016/05/045 . .

TY  - JOUR
AU  - Zakharov, Alexander F.
AU  - Borka, Duško
AU  - Borka Jovanović, Vesna
AU  - Jovanović, Predrag
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8601
AB  - Here we investigate possible applications of observed stellar orbits around Galactic Center for constraining the R-n gravity at Galactic scales. For that purpose, we simulated orbits of S2-like stars around the massive black hole at Galactic Center, and study the constraints on the R-n gravity which could be obtained by the present and next generations of large telescopes. Our results show that R-n gravity affects the simulated orbits in the qualitatively similar way as a bulk distribution of matter (including a stellar cluster and dark matter distributions) in Newtons gravity. In the cases where the density of extended mass is higher, the maximum allowed value of parameter beta in R-n gravity is noticeably smaller, due to the fact that the both extended mass and R-n gravity cause the retrograde orbital precession. (C) 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.
T2  - Advances in Space Research
T1  - Constraints on R-n gravity from precession of orbits of S2-like stars: A case of a bulk distribution of mass
VL  - 54
IS  - 6
SP  - 1108
EP  - 1112
DO  - 10.1016/j.asr.2014.05.027
ER  - 

@article{
author = "Zakharov, Alexander F. and Borka, Duško and Borka Jovanović, Vesna and Jovanović, Predrag",
year = "2014",
abstract = "Here we investigate possible applications of observed stellar orbits around Galactic Center for constraining the R-n gravity at Galactic scales. For that purpose, we simulated orbits of S2-like stars around the massive black hole at Galactic Center, and study the constraints on the R-n gravity which could be obtained by the present and next generations of large telescopes. Our results show that R-n gravity affects the simulated orbits in the qualitatively similar way as a bulk distribution of matter (including a stellar cluster and dark matter distributions) in Newtons gravity. In the cases where the density of extended mass is higher, the maximum allowed value of parameter beta in R-n gravity is noticeably smaller, due to the fact that the both extended mass and R-n gravity cause the retrograde orbital precession. (C) 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.",
journal = "Advances in Space Research",
title = "Constraints on R-n gravity from precession of orbits of S2-like stars: A case of a bulk distribution of mass",
volume = "54",
number = "6",
pages = "1108-1112",
doi = "10.1016/j.asr.2014.05.027"
}

Zakharov, A. F., Borka, D., Borka Jovanović, V.,& Jovanović, P.. (2014). Constraints on R-n gravity from precession of orbits of S2-like stars: A case of a bulk distribution of mass. in Advances in Space Research, 54(6), 1108-1112.
https://doi.org/10.1016/j.asr.2014.05.027

Zakharov AF, Borka D, Borka Jovanović V, Jovanović P. Constraints on R-n gravity from precession of orbits of S2-like stars: A case of a bulk distribution of mass. in Advances in Space Research. 2014;54(6):1108-1112.
doi:10.1016/j.asr.2014.05.027 .

Zakharov, Alexander F., Borka, Duško, Borka Jovanović, Vesna, Jovanović, Predrag, "Constraints on R-n gravity from precession of orbits of S2-like stars: A case of a bulk distribution of mass" in Advances in Space Research, 54, no. 6 (2014):1108-1112,
https://doi.org/10.1016/j.asr.2014.05.027 . .

TY  - JOUR
AU  - Zakharov, Alexander F.
AU  - Borka, Duško
AU  - Borka Jovanović, Vesna
AU  - Jovanović, Predrag
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/96
AB  - Here we investigate possible applications of observed stellar orbits around Galactic Center for constraining the R-n gravity at Galactic scales. For that purpose, we simulated orbits of S2-like stars around the massive black hole at Galactic Center, and study the constraints on the R-n gravity which could be obtained by the present and next generations of large telescopes. Our results show that R-n gravity affects the simulated orbits in the qualitatively similar way as a bulk distribution of matter (including a stellar cluster and dark matter distributions) in Newtons gravity. In the cases where the density of extended mass is higher, the maximum allowed value of parameter beta in R-n gravity is noticeably smaller, due to the fact that the both extended mass and R-n gravity cause the retrograde orbital precession. (C) 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.
T2  - Advances in Space Research
T1  - Constraints on R-n gravity from precession of orbits of S2-like stars: A case of a bulk distribution of mass
VL  - 54
IS  - 6
SP  - 1108
EP  - 1112
DO  - 10.1016/j.asr.2014.05.027
ER  - 

@article{
author = "Zakharov, Alexander F. and Borka, Duško and Borka Jovanović, Vesna and Jovanović, Predrag",
year = "2014",
abstract = "Here we investigate possible applications of observed stellar orbits around Galactic Center for constraining the R-n gravity at Galactic scales. For that purpose, we simulated orbits of S2-like stars around the massive black hole at Galactic Center, and study the constraints on the R-n gravity which could be obtained by the present and next generations of large telescopes. Our results show that R-n gravity affects the simulated orbits in the qualitatively similar way as a bulk distribution of matter (including a stellar cluster and dark matter distributions) in Newtons gravity. In the cases where the density of extended mass is higher, the maximum allowed value of parameter beta in R-n gravity is noticeably smaller, due to the fact that the both extended mass and R-n gravity cause the retrograde orbital precession. (C) 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.",
journal = "Advances in Space Research",
title = "Constraints on R-n gravity from precession of orbits of S2-like stars: A case of a bulk distribution of mass",
volume = "54",
number = "6",
pages = "1108-1112",
doi = "10.1016/j.asr.2014.05.027"
}

Zakharov, A. F., Borka, D., Borka Jovanović, V.,& Jovanović, P.. (2014). Constraints on R-n gravity from precession of orbits of S2-like stars: A case of a bulk distribution of mass. in Advances in Space Research, 54(6), 1108-1112.
https://doi.org/10.1016/j.asr.2014.05.027

Zakharov AF, Borka D, Borka Jovanović V, Jovanović P. Constraints on R-n gravity from precession of orbits of S2-like stars: A case of a bulk distribution of mass. in Advances in Space Research. 2014;54(6):1108-1112.
doi:10.1016/j.asr.2014.05.027 .

Zakharov, Alexander F., Borka, Duško, Borka Jovanović, Vesna, Jovanović, Predrag, "Constraints on R-n gravity from precession of orbits of S2-like stars: A case of a bulk distribution of mass" in Advances in Space Research, 54, no. 6 (2014):1108-1112,
https://doi.org/10.1016/j.asr.2014.05.027 . .

TY  - JOUR
AU  - Borka, Duško
AU  - Jovanović, Predrag
AU  - Borka Jovanović, Vesna
AU  - Zakharov, Alexander F.
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5776
AB  - We consider possible signatures for Yukawa gravity within the Galactic Central Parsec, based on our analysis of the S2 star orbital precession around the massive compact dark object at the Galactic Centre, and on the comparisons between the simulated orbits in Yukawa gravity and two independent sets of observations. Our simulations resulted in strong constraints on the range of Yukawa interaction Lambda and showed that its most probable value in the case of S2 star is around 5000 - 7000 AU. At the same time, we were not able to obtain reliable constrains on the universal constant delta of Yukawa gravity, because the current observations of S2 star indicated that it may be highly correlated with parameter Lambda in the range (0 LT delta LT 1). For delta GT 2 they are not correlated. However, the same universal constant which was successfully applied to clusters of galaxies and rotation curves of spiral galaxies (delta = 1/3) also gives a satisfactory agreement with the observed orbital precession of the S2 star, and in that case the most probable value for the scale parameter is Lambda approximate to 3000 +/- 1500 AU. Also, the Yukawa gravity potential induces precession of S2 star orbit in the same direction as General Relativity for delta GT 0 and for delta LT -1, and in the opposite direction for -1 LT delta LT 0. The future observations with advanced facilities, such as GRAVITY or/and European Extremely Large Telescope, are needed in order to verify these claims.
T2  - Journal of Cosmology and Astroparticle Physics
T1  - Constraining the range of Yukawa gravity interaction from S2 star orbits
IS  - 11
DO  - 10.1088/1475-7516/2013/11/050
ER  - 

@article{
author = "Borka, Duško and Jovanović, Predrag and Borka Jovanović, Vesna and Zakharov, Alexander F.",
year = "2013",
abstract = "We consider possible signatures for Yukawa gravity within the Galactic Central Parsec, based on our analysis of the S2 star orbital precession around the massive compact dark object at the Galactic Centre, and on the comparisons between the simulated orbits in Yukawa gravity and two independent sets of observations. Our simulations resulted in strong constraints on the range of Yukawa interaction Lambda and showed that its most probable value in the case of S2 star is around 5000 - 7000 AU. At the same time, we were not able to obtain reliable constrains on the universal constant delta of Yukawa gravity, because the current observations of S2 star indicated that it may be highly correlated with parameter Lambda in the range (0 LT delta LT 1). For delta GT 2 they are not correlated. However, the same universal constant which was successfully applied to clusters of galaxies and rotation curves of spiral galaxies (delta = 1/3) also gives a satisfactory agreement with the observed orbital precession of the S2 star, and in that case the most probable value for the scale parameter is Lambda approximate to 3000 +/- 1500 AU. Also, the Yukawa gravity potential induces precession of S2 star orbit in the same direction as General Relativity for delta GT 0 and for delta LT -1, and in the opposite direction for -1 LT delta LT 0. The future observations with advanced facilities, such as GRAVITY or/and European Extremely Large Telescope, are needed in order to verify these claims.",
journal = "Journal of Cosmology and Astroparticle Physics",
title = "Constraining the range of Yukawa gravity interaction from S2 star orbits",
number = "11",
doi = "10.1088/1475-7516/2013/11/050"
}

Borka, D., Jovanović, P., Borka Jovanović, V.,& Zakharov, A. F.. (2013). Constraining the range of Yukawa gravity interaction from S2 star orbits. in Journal of Cosmology and Astroparticle Physics(11).
https://doi.org/10.1088/1475-7516/2013/11/050

Borka D, Jovanović P, Borka Jovanović V, Zakharov AF. Constraining the range of Yukawa gravity interaction from S2 star orbits. in Journal of Cosmology and Astroparticle Physics. 2013;(11).
doi:10.1088/1475-7516/2013/11/050 .

Borka, Duško, Jovanović, Predrag, Borka Jovanović, Vesna, Zakharov, Alexander F., "Constraining the range of Yukawa gravity interaction from S2 star orbits" in Journal of Cosmology and Astroparticle Physics, no. 11 (2013),
https://doi.org/10.1088/1475-7516/2013/11/050 . .

TY  - JOUR
AU  - Borka, Duško
AU  - Jovanović, Predrag
AU  - Borka Jovanović, Vesna
AU  - Zakharov, Alexander F.
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4868
AB  - We study some possible observational signatures of R-n gravity at Galactic scales and how these signatures could be used for constraining this type of f(R) gravity. For that purpose, we performed two-body simulations in the R-n gravity potential and analyzed the obtained trajectories of S2-like stars around the Galactic center, as well as the resulting parameter space of the Rn gravity potential. Here, we discuss the constraints on Rn gravity which can be obtained from the observations of orbits of S2-like stars with the present and next generations of large telescopes. We make comparisons between the theoretical results and observations. Our results show that the most probable value for the parameter r(c) in the Rn gravity potential in the case of S2-like stars is similar to 100 AU, while the universal parameter beta is close to 0.01. Also, the gravity potential induces the precession of S2-like star orbits in the opposite direction with respect to general relativity; therefore, such a behavior of orbits is qualitatively similar to the behavior of Newtonian orbits with a bulk distribution of matter (including a stellar cluster and dark matter distributions).
T2  - Physical Review D
T1  - Constraints on R-n gravity from precession of orbits of S2-like stars
VL  - 85
IS  - 12
DO  - 10.1103/PhysRevD.85.124004
ER  - 

@article{
author = "Borka, Duško and Jovanović, Predrag and Borka Jovanović, Vesna and Zakharov, Alexander F.",
year = "2012",
abstract = "We study some possible observational signatures of R-n gravity at Galactic scales and how these signatures could be used for constraining this type of f(R) gravity. For that purpose, we performed two-body simulations in the R-n gravity potential and analyzed the obtained trajectories of S2-like stars around the Galactic center, as well as the resulting parameter space of the Rn gravity potential. Here, we discuss the constraints on Rn gravity which can be obtained from the observations of orbits of S2-like stars with the present and next generations of large telescopes. We make comparisons between the theoretical results and observations. Our results show that the most probable value for the parameter r(c) in the Rn gravity potential in the case of S2-like stars is similar to 100 AU, while the universal parameter beta is close to 0.01. Also, the gravity potential induces the precession of S2-like star orbits in the opposite direction with respect to general relativity; therefore, such a behavior of orbits is qualitatively similar to the behavior of Newtonian orbits with a bulk distribution of matter (including a stellar cluster and dark matter distributions).",
journal = "Physical Review D",
title = "Constraints on R-n gravity from precession of orbits of S2-like stars",
volume = "85",
number = "12",
doi = "10.1103/PhysRevD.85.124004"
}

Borka, D., Jovanović, P., Borka Jovanović, V.,& Zakharov, A. F.. (2012). Constraints on R-n gravity from precession of orbits of S2-like stars. in Physical Review D, 85(12).
https://doi.org/10.1103/PhysRevD.85.124004

Borka D, Jovanović P, Borka Jovanović V, Zakharov AF. Constraints on R-n gravity from precession of orbits of S2-like stars. in Physical Review D. 2012;85(12).
doi:10.1103/PhysRevD.85.124004 .

Borka, Duško, Jovanović, Predrag, Borka Jovanović, Vesna, Zakharov, Alexander F., "Constraints on R-n gravity from precession of orbits of S2-like stars" in Physical Review D, 85, no. 12 (2012),
https://doi.org/10.1103/PhysRevD.85.124004 . .