Testing General Relativity with Stellar Orbits around the Supermassive Black Hole in Our Galactic Center

Black holes up close

Recent developments have ushered in a new era in the field of black-hole astrophysics, providing a direct view of the remarkable environment near black-hole event horizons. These observations have enabled astronomers to confirm long-standing ideas on the physics of gas flowing into black holes with temperatures that are hundreds of times greater than at the centre of the Sun. At the same time, the observations have conclusively shown that light rays near a black hole experience large deflections that cause a dark shadow in the centre of the image, an effect predicted by Einstein's theory of general relativity. With further investment, this field is poised to deliver decades of advances in our understanding of gravity and black holes through stringent tests of general relativity, as well as insights into the role of black holes as the central engines powering a wide range of astronomical phenomena.

Investigating the nature of mass distribution surrounding the Galactic supermassive black hole

In the past three decades, many stars orbiting about the supermassive black hole (SMBH) at the Galactic Centre (Sgr A*) were identified. Their orbital nature can give stringent constraints for the mass of the SMBH. In particular, the star S2 has completed at least one period since our first detection of its position, which can provide rich information to examine the properties of the SMBH, and the astrophysical environment surrounding the SMBH. Here, we report an interesting phenomenon that if a significant amount of dark matter or stellar mass is distributed around the SMBH, the precession speed of the S2 stellar orbit could be ‘slow down’ by at most 27% compared with that without dark matter surrounding the SMBH, assuming the optimal dark matter scenario. We anticipate that future high quality observational data of the S2 stellar orbit or other stellar orbits can help reveal the actual mass distribution near the SMBH and the nature of dark matter.

Bound Orbits and Epicyclic Motions around Renormalization Group Improved Schwarzschild Black Holes

We study timelike particles’ bound orbits around renormalization group improved Schwarzschild black holes (RGISBHs), which originate from renormalization group improvement of the Einstein–Hilbert action by using the running Newton constant. By considering the secular periastron precession for the timelike particles orbiting around RGISBHs, we found that it is not feasible to distinguish such black holes from Schwarzschild ones in the weak gravitational field. However, in the strong gravitational field, periodic orbits for the particles are investigated by employing a taxonomy. This suggests that the variation of the parameters in RGISBHs can change the taxonomy. This leads to a transition from periodic motion around Schwarzschild black holes to a quasi-periodic motion around these black holes. After that, the epicyclic motions of charged particles around RGISBHs immersed in an external asymptotically uniform magnetic field are taken into account with respect to the observed twin peak quasi-periodic oscillations’ frequencies. The epicyclic motions of charged particles around such black holes in the external magnetic field can give one possible explanation for the 3:2 resonance in three low-mass X-ray binaries. Our results might provide some hints to distinguish RGISBHs from the classical black holes by using periodic orbits and epicyclic motions around the strong gravitational field.

Estimating the Parameters of the Hybrid Palatini Gravity Model with the Schwarzschild Precession of S2, S38 and S55 Stars: Case of Bulk Mass Distribution

We estimate the parameters of the Hybrid Palatini gravity model with the Schwarzschild precession of S-stars, specifically of the S2, S38 and S55 stars. We also take into account the case of bulk mass distribution near the Galactic Center. We assume that the Schwarzschild orbital precession of mentioned S-stars is the same as in General Relativity (GR) in all studied cases. 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. The astronomical data analysis of S38 and S55 orbits showed that, also in these cases, the orbital precession is close to the GR prediction. Based on this observational fact, we evaluated the parameters of the Hybrid Palatini Gravity model with the Schwarzschild precession of the S2, S38 and S55 stars, and we estimated the range of parameters of the Hybrid Palatini gravity model for which the orbital precession is as in GR for all three stars. We also evaluated the parameters of the Hybrid Palatini Gravity model in the case of different values of bulk mass density distribution of extended matter. We believe that proposed method is a useful tool to evaluate parameters of the gravitational potential at the Galactic Center.

Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star

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.

Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories

Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providing the adequate formalism for metric-affine theories of gravity with curvature, torsion and non-metricity. In this paper, we analyze the structure of gauge theories of gravity and consider the relation between fundamental geometrical objects and symmetry principles as well as different spacetime paradigms. Special attention is given to Poincaré gauge theories of gravity, their field equations and Noether conserved currents, which are the sources of gravity. We then discuss several topics of the gauge approach to gravitational phenomena, namely, quadratic Poincaré gauge models, the Einstein-Cartan-Sciama-Kibble theory, the teleparallel equivalent of general relativity, quadratic metric-affine Lagrangians, non-Lorentzian connections, and the breaking of Lorentz invariance in the presence of non-metricity. We also highlight the probing of post-Riemannian geometries with test matter. Finally, we briefly discuss some perspectives regarding the role of both geometrical methods and symmetry principles towards unified field theories and a new spacetime paradigm, motivated from the gauge approach to gravity.

Null and Timelike Geodesics near the Throats of Phantom Scalar Field Wormholes

We study geodesic motion near the throats of asymptotically flat, static, spherically symmetric traversable wormholes supported by a self-gravitating minimally coupled phantom scalar field with an arbitrary self-interaction potential. We assume that any such wormhole possesses the reflection symmetry with respect to the throat, and consider only its observable “right half”. It turns out that the main features of bound orbits and photon trajectories close to the throats of such wormholes are very different from those near the horizons of black holes. We distinguish between wormholes of two types, the first and second ones, depending on whether the redshift metric function has a minimum or maximum at the throat. First, it turns out that orbits located near the centre of a wormhole of any type exhibit retrograde precession, that is, the angle of pericentre precession is negative. Second, in the case of high accretion activity, wormholes of the first type have the innermost stable circular orbit at the throat while those of the second type have the resting-state stable circular orbit in which test particles are at rest at all times. In our study, we have in mind the possibility that the strongly gravitating objects in the centres of galaxies are wormholes, which can be regarded as an alternative to black holes, and the scalar field can be regarded as a realistic model of dark matter surrounding galactic centres. In this connection, we discuss qualitatively some observational aspects of results obtained in this article.

Search for a Variation of the Fine Structure Constant around the Supermassive Black Hole in Our Galactic Center

Searching for space-time variations of the constants of Nature is a promising way to search for new physics beyond general relativity and the standard model motivated by unification theories and models of dark matter and dark energy. We propose a new way to search for a variation of the fine-structure constant using measurements of late-type evolved giant stars from the S star cluster orbiting the supermassive black hole in our Galactic Center. A measurement of the difference between distinct absorption lines (with different sensitivity to the fine structure constant) from a star leads to a direct estimate of a variation of the fine structure constant between the star's location and Earth. Using spectroscopic measurements of five stars, we obtain a constraint on the relative variation of the fine structure constant below 10^{-5}. This is the first time a varying constant of nature is searched for around a black hole and in a high gravitational potential. This analysis shows new ways the monitoring of stars in the Galactic Center can be used to probe fundamental physics.

Constraining the Mass of the Graviton with the Planetary Ephemeris INPOP

We use the planetary ephemeris INPOP17b to constrain the existence of a Yukawa suppression to the Newtonian potential, generically associated with the graviton's mass. We also give an interpretation of this result for a specific case of fifth force framework. We find that the residuals for the Cassini spacecraft significantly (90% C.L.) degrade for Compton wavelengths of the graviton smaller than 1.83×10^{13}  km, which correspond to a graviton mass bigger than 6.76×10^{-23}  eV/c^{2}. This limit is comparable in magnitude to the one obtained by the LIGO-Virgo Collaboration in the radiative regime. We also use this specific example to defend that constraints on alternative theories of gravity obtained from postfit residuals may be generically overestimated.

The Unique Blazar OJ 287 and Its Massive Binary Black Hole Central Engine

The bright blazar OJ 287 is the best-known candidate for hosting a nanohertz gravitational wave (GW) emitting supermassive binary black hole (SMBBH) in the present observable universe. The binary black hole (BBH) central engine model, proposed by Lehto and Valtonen in 1996, was influenced by the two distinct periodicities inferred from the optical light curve of OJ 287. The current improved model employs an accurate general relativistic description to track the trajectory of the secondary black hole (BH) which is crucial to predict the inherent impact flares of OJ 287. The successful observations of three predicted impact flares open up the possibility of using this BBH system to test general relativity in a hitherto unexplored strong field regime. Additionally, we briefly describe an ongoing effort to interpret observations of OJ 287 in a Bayesian framework.

Alternative Uses for Quantum Systems and Devices

Quantum optical systems and devices were analyzed to verify theories both predicting new particles on flat spacetime, and for the verification of Planck-scale physics for cosmological investigation.

Modified gravity revealed along geodesic tracks

The study of the dynamics of a two-body system in modified gravity constitutes a more complex problem than in Newtonian gravity. Numerical methods are typically needed to solve the equations of geodesics. Despite the complexity of the problem, the study of a two-body system in f(R) gravity leads to a new exciting perspective hinting the right strategy to adopt in order to probe modified gravity. Our results point out some differences between the semiclassical (Newtonian) approach, and the relativistic (geodesic) one thus suggesting that the latter represents the best strategy for future tests of modified theories of gravity. Finally, we have also highlighted the capability of forthcoming observations to serve as smoking gun of modified gravity revealing a departure from GR or further reducing the parameter space of f(R) gravity.

Constraints on alternative theories of gravity with observations of the Galactic Center

To evaluate a potential usually one analyzes trajectories of test particles. For the Galactic Center case astronomers use bright stars or photons, so there are two basic observational techniques to investigate a gravitational potential, namely, (a) monitoring the orbits of bright stars near the Galactic Center as it is going on with 10m Keck twin and four 8m VLT telescopes equipped with adaptive optics facilities (in addition, recently the IR interferometer GRAVITY started to operate with VLT); (b) measuring the size and shape of shadows around black hole with VLBI-technique using telescopes operating in mm-band. At the moment, one can use a small relativistic correction approach for stellar orbit analysis, however, in the future the approximation will not be precise enough due to enormous progress of observational facilities and recently the GRAVITY team found that the first post-Newtonian correction has to be taken into account for the gravitational redshift in the S2 star orbit case. Meanwhile for smallest structure analysis in VLBI observations one really needs a strong gravitational field approximation. We discuss results of observations and their interpretations. In spite of great efforts there is a very slow progress to resolve dark matter (DM) and dark energy (DE) puzzles and in these circumstances in last years a number of alternative theories of gravity have been proposed. Parameters of these theories could be effectively constrained with of observations of the Galactic Center. We show some cases of alternative theories of gravity where their parameters are constrained with observations, in particular, we consider massive theory of gravity. We choose the alternative theory of gravity since there is a significant activity in this field and in the last years theorists demonstrated an opportunity to create such theories without ghosts, on the other hand, recently, the joint LIGO & Virgo team presented an upper limit on graviton mass such as mg< 1:2 × 10-22eV [1] analyzing gravitational wave signal in their first paper where they reported about the discovery of gravitational waves from binary black holes as it was suggested by C. Will [2]. So, the authors concluded that their observational data do not indicate a significant deviation from classical general relativity. We show that an analysis of bright star trajectories could estimate a graviton mass with a commensurable accuracy in comparison with an approach used in gravitational wave observations and the estimates obtained with these two approaches are consistent. Therefore, such an 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. We showed that in the future graviton mass estimates obtained with analysis of trajectories of bright stars would be better than current LIGO bounds on the value, therefore, based on a potential reconstruction at the Galactic Center we obtain bounds on a graviton mass and these bounds are comparable with LIGO constraints. Analyzing size of shadows around the supermassive black hole at the Galactic Center (or/and in the center of M87) one could constrain parameters of different alternative theories of gravity as well.

Constraints on tidal charge of the supermassive black hole at the Galactic Center with trajectories of bright stars

As it was pointed out recently in Hees et al. (Phys Rev Lett 118:211101, 2017), observations of stars near the Galactic Center with current and future facilities provide an unique tool to test general relativity (GR) and alternative theories of gravity in a strong gravitational field regime. In particular, the authors showed that the Yukawa gravity could be constrained with Keck and TMT observations. Some time ago, Dadhich et al. (Phys Lett B 487:1, 2001) showed that the Reissner-Nordström metric with a tidal charge is naturally appeared in the framework of Randall-Sundrum model with an extra dimension ( Q 2 is called tidal charge and it could be negative in such an approach). Astrophysical consequences of presence of black holes with a tidal charge are considerered, in particular, geodesics and shadows in Kerr-Newman braneworld metric are analyzed in Schee and Stuchlík (Intern J Mod Phys D 18:983, 2009), while profiles of emission lines generated by rings orbiting braneworld Kerr black hole are considered in Schee and Stuchlík (Gen Relat Grav 52:1795, 2009). Possible observational signatures of gravitational lensing in a presence of the Reissner-Nordström black hole with a tidal charge at the Galactic Center are discussed in papers (Bin-Nun in Phys Rev D 81:123011, 2010; Bin-Nun in Phys Rev D 82:064009, 2010; Bin-Nun in Class Quant Grav 28:114003, 2011). Here we are following such an approach and we obtain analytical expressions for orbital precession for Reissner-Nordström-de-Sitter solution in post-Newtonian approximation and discuss opportunities to constrain parameters of the metric from observations of bright stars with current and future astrometric observational facilities such as VLT, Keck, GRAVITY, E-ELT and TMT.

Perspectives on Constraining a Cosmological Constant-Type Parameter with Pulsar Timing in the Galactic Center

Independent tests aiming to constrain the value of the cosmological constant Λ are usually difficult because of its extreme smallness ( Λ ≃ 1 × 10 - 52 m - 2 , or 2 . 89 × 10 - 122 in Planck units ) . Bounds on it from Solar System orbital motions determined with spacecraft tracking are currently at the ≃ 10 - 43 – 10 - 44 m - 2 ( 5 – 1 × 10 - 113 in Planck units ) level, but they may turn out to be optimistic since Λ has not yet been explicitly modeled in the planetary data reductions. Accurate ( σ τ p ≃ 1 – 10 μ s ) timing of expected pulsars orbiting the Black Hole at the Galactic Center, preferably along highly eccentric and wide orbits, might, at least in principle, improve the planetary constraints by several orders of magnitude. By looking at the average time shift per orbit Δ δ τ ¯ p Λ , an S2-like orbital configuration with e = 0 . 8839 , P b = 16 yr would permit a preliminarily upper bound of the order of Λ ≲ 9 × 10 - 47 m - 2 ≲ 2 × 10 - 116 in Planck units if only σ τ p were to be considered. Our results can be easily extended to modified models of gravity using Λ -type parameters.