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Abstract <p>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.</p>

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On the Shadows of Black Holes in Non-Einsteinian Theories of Gravity

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • A. F. Zakharov

摘要

Abstract

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.