Phenomenological Extension for Tidal Charge Black Hole
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I, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Phenomenological Extension for Tidal Charge Black Hole1 S. O. Alexeyeva,b,*, B. N. Latoshc,d, V. A. Prokopova,e,**, and E. D. Emtsovaa,e a Sternberg
Astronomical Institute, Moscow State University, Moscow, 119234 Russia Department of Quantum Theory and High Energy Physics, Physics Faculty, Moscow State University, Moscow, 119234 Russia c Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH, United Kingdom d Dubna State University, Dubna, 141982 Russia e Department of Astrophysics and Stellar Astronomy, Physics Faculty, Moscow State University, Moscow, 119234 Russia *e-mail: [email protected] **e-mail: [email protected] b
Received December 6, 2018; revised December 10, 2018; accepted December 11, 2018
Abstract—A simple phenomenological extension of the black hole solution with tidal charge is proposed. Empirical data on the Sgr A* black hole is consistent with the suggested metric which serves as a generalization of the Reissner–Nordström one. Such a generalization includes the leading effects beyond general relativity; so, the discussed metric can explain wider range of gravitational effects. We discuss physical features of an object described by the proposed metric, namely, the size of its shadow and the innermost stable circular orbit radius. DOI: 10.1134/S1063776119040010
1. INTRODUCTION General Relativity (GR) is admitted to be the best theory of gravity, as it provides a correct description of multiple gravitational phenomena [1, 2]. At the same time the existence of dark matter and dark energy provides a ground to consider GR as a relevant theory only on small spacial scales [3–5]. Basic physical principles that may be used to modify GR are well-understood and widely implemented in so-called modified gravity models [6, 7]. The spectrum of these models includes multiple f(R) gravity and scalar-tensor models, including Horndeski models [8–10]. A particular modify gravity model can be considered as a suitable generalization of GR, if it imporves description of gravitational phenomena at least at one spacial scale. Because of this feature one is only interested in modified gravity models that passes Solar system tests, for instance, such a model should have postNewtonian parameters (and post-Keplerian parameters for binary pulsars) consistent with the current empirical data [1, 7, 11]. Within GR a non-rotating black hole without electric charge is described by the Schwarzschild metric. At the same time recent results [12] show that the Reissner–Nordström metric with non-vanishing charge is consistent with the empirical data from Sgr A* black hole [13–15]. There are strong theoretical 1 The article is published in the original.
evidences that a real “astrophysical” black hole cannot have a significant electric charge. At the same time modified gravity models, namely, Randall–Sundrum one, predict that a metric similar to the Reissner– Nordström one serves as an exact solution of corresponding field equations [16]. Such a solution d
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