Alexander Fyodorovich Zakharov

NICA is a tool to investigate the early Universe in laboratory. It would be reasonable to recall some essential issues in physical cosmology development. GR was created by A. Einstein in 1915. In 1917 Einstein proposed the first (static) cosmological model. Later A. Eddington proved that the model is unstable therefore it can not be realizable in nature. In 1922 and 1924 A.A. Friedmann found non-stationary solutions for cosmological equations written in the framework of GR. In 1927 G. Lemaître obtained very similar results and, in addition, he derived the Hubble law (E. Hubble obtained this law from observations). Unfortunately, G. Lemaître published his paper in not very popular Belgium journal. In 1931 Lemaître proposed the first version of hot Universe model (he called it hypothesis of the primeval atom). In his book “The Primeval Atom—An Essay on Cosmogony” Lemaître predicted even a background radiation as a signature of his model. At the end of 1940s G. Gamow and his students proposed their hot universe model where he explained primordial nucleosythesis of helium at the initial stage of the Universe evolution. One of the features of Lemaître–Gamow model was an existence of CMB radiation with a temperature around a few K. It was recalled that the discovery of CMB radiation was done by T. Shmaonov in 1956 and his paper was published in 1957 (several years before the discovery done by Penzias and Wilson). In 1965, 1970 E.B. Gliner proposed vacuum like equation of matter which could correspond to exponential explosion of the Universe which was later called inflation. For decades in USSR, A.A. Friedmann’s cosmologocal non-stationary models were treated as purely mathematical results without cosmological and astronomical applications. On September 16, 1925 Friedmann passed away untimely and it would be reasonable to remind today his great contribution in physical cosmology since the authors book on Friedmann wrote “Similarly to Copernicus who forced the Earth to move, Friedmann forced the Universe to expand.”

In the paper, graviton mass constraints are obtained by analyzing the trajectory of a bright star in the vicinity of the center of our Galaxy, using observations from the GRAVITY and Keck groups. Other astronomical ways to limit the graviton mass are briefly discussed.

In a recent article by S.O. Alexeyev et al. (published in the journal Physics of Elementary Particles and Atomic Nuclei), the authors claim that they are discussing the possibility of estimating the parameters of black hole shadows that may arise in the Horndeski model and bumblebee gravity. Leaving aside the question that none of the proposed alternative theories of gravity can be considered preferable to Einstein’s general theory of relativity, it should be noted that the authors have not shown that they have found rotating solutions of the black hole type in the non-Einsteinian theories of gravity that they are considering. As is known, the procedure for taking rotation into account proposed by Newman–Janis was applied to “obtain” the Kerr metric from the Schwarzschild metric within the framework of GR. Later, several authors showed that for a large number of cases of non-Einsteinian gravity theories, the Newman–Janis algorithm cannot be used to obtain analogues of Kerr-type solutions in such gravity theories. Therefore, for each version of an alternative theory of gravity, it is necessary to prove that the Newman–Janis procedure actually yields a Kerr-type solution in the non-Einsteinian theory of gravity under consideration. Moreover, it should be noted that in the discussed work, Alexeyev et al. essentially considered a set of impact parameters corresponding to unstable circular photon orbits, and the fact that the corresponding motion parameters determine the shape and size of shadows remained unproven for the considered solutions such as black holes in alternative theories of gravity. That the problem of finding the shape and size of the shadow and the problem of finding circular photon orbits for Kerr black holes are equivalent was shown more than 20 years ago in a paper by Zakharov et al. published in the journal New Astronomy, where it was also noted that the shadow of a black hole in the Galactic Center can be reconstructed using VLBI observations from interferometers operating in the millimeter and submillimeter range. In recent years, a number of recent works have shown that for some generalizations of the Kerr–Newman metric, the presence of circular photon orbits is possible in the absence of shadows, so it is not justified to talk about the presence and properties of shadows only on the basis of considering circular photon orbits, as is argued in the work of Alexeyev et al.

Ограничения массы гравитона получены путем анализа траектории движения яркой звезды вблизи центра нашей Галактики с использованием наблюдений групп GRAVITY и Keck. Кратко обсуждаются другие астрономические способы оценки массы гравитона.

The possibility of estimating the parameters of alternative gravity theories from observations of galactic cluster “turnaround points” has been discussed in a recent publication. It was assumed that the gravitational field of a galactic cluster in the standard version of general relativity is described by the Schwarzschild-de Sitter metric. The authors of this paper asserted that they had obtained estimates of the parameters of alternative gravity theories from observations of galactic clusters, but no comparison of the theory with observations was made in the paper, and the authors assumed that the theoretical description of turning points in GR and the alternative theories under consideration should be similar. In this study, we conclude that theoretical models such as static spherical black holes can hardly be used to obtain constraints on the parameters of alternative gravity theories by analyzing the differences in the turning radii in these theories and GR, based on observations of galactic clusters.

General Relativity (GR) was created in November 1915, and since its creation this theory has undergone many tests. The first realistic cosmological models were proposed in the works of Friedmann, written in the 1920s. For a long time, Friedmann’s cosmological works were actually banned in the Soviet Union due to philosophical reasons, since the models where the birth and evolution of the Universe occurs were considered ideologically unacceptable. Due to great achievements in relativity and cosmology and due to increasing interest in these branches of science in the last decades, we recall the development of relativistic astrophysics and contribution of Russian researchers to these studies. Since one of the world leaders in physical cosmology A. A. Friedmann passed away in September 1925, it is reasonable to outline the main achievements of physical cosmology over the past 100 years. We also discuss observational and theoretical achievements in confirmations of relativistic observational predictions for black holes, including the closest supermassive black hole in our Galactic Center. We outline the evolution of black hole shadow from the purely theoretical concept to observable quantities for supermassive black holes in Sgr A* and M87*.

In our paper published in 2005, it was predicted that the shadow near the Galactic Center (GC) black hole could be reconstructed from results of observations of the global VLBI system operating in the millimeter or submillimeter range. This prediction became reality in 2022, when shadows near black holes in the GC and the center of the galaxy M87 (in 2019) were reconstructed from data of observations of the Event Horizon Telescope collaboration, and these results led to the appearance of a large number of theoretical papers that considered constraints on both alternative models of galactic centers and alternative theories of gravity. For Schwarzschild, Kerr, and Reissner–Nordström black holes, the impact parameters corresponding to circular photon orbits determine the shadow shape and size; however, as was shown in the abovementioned paper, in the cases of some metrics, the existence of circular photon orbits is possible, though shadows for these metrics are not formed. A number of recent papers (including one published in the journal PEPAN Letters) have put forth, without evidence, alternative models of galactic centers in which parameters corresponding to circular photon orbits determine the shadow shape and size.

In 2005 Zakharov et al. predicted an opportunity to reconstruct a shadow in Sgr A* with ground based or space—ground interferometer acting in mm or sub-mm band (the Millimetron was mentioned for such needs). The prediction was confirmed in May 2022 since the Event Horizon Telescope (EHT) Collaboration presented results of a shadow reconstruction for our Galactic Center (the shadow around the supermassive black hole in M87 was reconstructed in 2019). These reconstructions were based on EHT observations done in 2017. In 2005 Zakharov et al. also derived analytical expressions for shadow size as a function of charge for Reissner–Nordström metric and later these results were generalized for a tidal charge case. We discuss opportunities to evaluate parameters of alternative theories of gravity with shadow size estimates done by the EHT Collaboration, in particular, a tidal charge could be estimated from these observations. We also discuss opportunities to use Millimetron facilities for shadow reconstructions in M87* and Sgr A*. In our recent studies we discuss shadow formations for cases where naked singularities, wormholes or more exotic models substitute conventional black holes in galactic centers.

Despite the fact that several alternative theories of gravity have been proposed, (many of them have been suggested in the recent years) the general relati