Dusko Borka

In this paper, we investigated the capability of Yukawa gravity to explain the Schwarzschild precession of S-stars as a probe for General Relativity and to map the allowed parameter space of a potential fifth force. We simulated the S38 star orbit in a Yukawa gravity model and fitted it into the observed astronomical data of the S38 star using the Markov Chain Monte Carlo method in order to constrain the parameters (strength $\delta$ and range $\lambda$) of the Yukawa interaction. Comparing these findings with previous results for the S2 star reveals that the best-fit values for $\lambda$ are remarkably close, while the magnitudes of $\delta$ are slightly smaller for S38. These results map the joint statistical boundaries of a fifth force at the Galactic Center. Although the General Relativity limit ($\delta =0$) falls well within the reported $1\sigma$ uncertainties, rendering potential nominal deviations statistically insignificant, the interaction range $\lambda$ exhibits a highly stable spatial scale across different stellar orbits. This cross-consistency between independent datasets, with stable clusters near 360, 1900, and 7000 AU, keeps a viable physical window open for a fifth force. This agreement demonstrates that the interaction scale is robust against individual single-orbit systematic errors, ensuring that this parameter domain remains a prime target for future high-precision astrometric observations. Ultimately, analyzing S-star kinematics within Yukawa gravity provides a powerful independent tool for testing General Relativity and bounding non-standard gravitational effects at the Galactic Center.

Here we investigate a possible presence of a fifth force at the Galactic Center (GC), and its potential influence on the stellar orbits around the central supermassive black hole (SMBH) of our Galaxy. For this purpose we simulated the stellar orbits in a Yukawa gravity model that predicts the emergence of a fifth force, and fitted them into the observed orbit of S2 star around Sgr A* at the GC. The fitting was performed using Markov chain Monte Carlo (MCMC) method which enabled us to constrain the parameters of Yukawa interaction describing the strength $\delta$ and the range $\lambda$ of a fifth force. We studied the following cases for a fifth force range $\lambda$: (i) when it is about a few hundred AU (i.e., deep inside the orbit of S2 star), (ii) when it is about a thousand AU (i.e., approximately the size of S2 star orbit), and (iii) when it is several thousand AU (i.e., much larger than the size of S2 star orbit). The obtained results showed that as the range $\lambda$ of a fifth force increases, its strength $\delta$ also increases and relative error $\Delta \delta /\delta$ decreases. The resulting fifth-force strengths in all three cases are respectively: $\delta$∼0.005, 0.02 and 0.15. These results are consistent with the corresponding results of both our previous studies and those of other authors, regardless of the different Yukawa-like potentials used to model a fifth force. In addition, assuming that the orbital precession of S2 star is close to the prediction of General Relativity (GR) for its Schwarzschild precession, we studied whether the possible small discrepancies from this prediction could be also caused by a fifth force. For this purpose we used the $f_{\mathrm{SP}}$ parameter that was recently measured in the case of S2 star by GRAVITY Collaboration in 2020, and that describes the extent to which some gravitational model is relativistic. We found that the obtained estimates in all three cases are compatible, within the error intervals, with the measured value of $f_{\mathrm{SP}}=1.10\pm 0.19$.

Here we use the samples of spiral and elliptical galaxies, in order to investigate theoretically some of their properties and to test the empirical relations, in the light of modified gravities. We show that the baryonic Tully-Fisher relation can be described in the light of $f(R)$ gravity, without introducing the dark matter. Also, it is possible to explain the features of fundamental plane of elliptical galaxies without the dark matter hypothesis.

In this paper we use a modification of the Newtonian gravitational potential with a non-linear Yukawa-like correction, as it was proposed by C. Will earlier to obtain new bounds on graviton mass from the observed orbits of S-stars around the Galactic Center (GC). This phenomenological potential differs from the gravitational potential obtained in the weak field limit of Yukawa gravity, which we used in our previous studies. We also assumed that the orbital precession of S-stars is close to the prediction of General Relativity (GR) for Schwarzschild precession, but with a possible small discrepancy from it. This assumption is motivated by the fact that the GRAVITY Collaboration in 2020 and in 2022 detected Schwarzschild precession in the S2 star orbit around the Supermassive Black Hole (SMBH) at the GC. Using this approach, we were able to constrain parameter $λ$ of the potential and, assuming that it represents the graviton Compton wavelength, we also found the corresponding upper bound of graviton mass. The obtained results were then compared with our previous estimates, as well as with the estimates of other authors.

In this paper we use a modification of the Newtonian gravitational potential with a non-linear Yukawa-like correction, as it was proposed by C. Will earlier to obtain new bounds on graviton mass from the observed orbits of S-stars around the Galactic Center (GC). This phenomenological potential differs from the gravitational potential obtained in the weak field limit of Yukawa gravity, which we used in our previous studies. We also assumed that the orbital precession of S-stars is close to the prediction of General Relativity (GR) for Schwarzschild precession, but with a possible small discrepancy from it. This assumption is motivated by the fact that the GRAVITY Collaboration in 2020 and in 2022 detected Schwarzschild precession in the S2 star orbit around the Supermassive Black Hole (SMBH) at the GC. Using this approach, we were able to constrain parameter $\lambda$ of the potential and, assuming that it represents the graviton Compton wavelength, we also found the corresponding upper bound of graviton mass. The obtained results were then compared with our previous estimates, as well as with the estimates of other authors.

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 $\mathrm{\Lambda }$. From the obtained values of $\mathrm{\Lambda }$, 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.

Here we study possible improvements of the existing constraints on the upper bound of graviton mass by the analysis of the stellar orbits around the SMBH at the 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 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 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 upper bounds on the graviton mass. It is also demonstrated that such 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.