Hybrid Metric-Palatini Gravity: Black Holes, Wormholes, Singularities, and Instabilities
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Hybrid Metric-Palatini Gravity: Black Holes, Wormholes, Singularities, and Instabilities K. A. Bronnikov1, 2, 3* , S. V. Bolokhov2** , and M. V. Skvortsova2*** 1
2
Center for Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya ul. 46, Moscow, 119361 Russia Institute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, Moscow, 117198 Russia 3 National Research Nuclear University “MEPhI,” Kashirskoe sh. 31, Moscow, 115409 Russia Received April 22, 2020; revised May 10, 2020; accepted May 12, 2020
Abstract—The hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. We discuss static, spherically symmetric vacuum solutions of HMPG with the aid of its scalar-tensor theory (STT) representation. This scalar-tensor theory coincides with general relativity with a conformally coupled scalar field (which can be canonical or phantom), therefore the known solutions of this theory are re-interpreted in terms of HMPG. In particular, in the case of zero scalar field potential V (φ), such that both Riemannian and Palatini Ricci scalars are zero, generic asymptotically flat solutions either contain naked singularities or describe traversable wormholes, and there are only special cases of black hole solutions with extremal horizons. There is also a one-parameter family of solutions with an infinite number of extremal horizons between static regions. Examples of analytical solutions with nonzero potentials V (φ) are also described, among them black hole solutions with simple horizons which are generic but, for canonical scalars, they require (at least partly) negative potentials. With phantom scalars there are “black universe” solutions that lead beyond the horizon to an expanding universe instead of a singularity. Most of the solutions under consideration turn out to be unstable under scalar monopole perturbations, but some special black hole solutions are stable. DOI: 10.1134/S0202289320030044
1. INTRODUCTION General relativity (GR) that has recently celebrated its century, is known to still successfully describe all local observational effects. It is however, unable to completely account for large-scale phenomena, facing the so-called Dark Matter and Dark Energy problems. There are two alternative ways in addressing these problems: one is still to adhere to GR but to introduce so far unobserved forms of matter like WIMPs (weakly interacting massive particles) as Dark Matter, and a cosmological constant or a “quintessence” scalar field, etc., as Dark Energy [1]. An alternative approach is to modify GR itself, considering more general Lagrangian functions (for instance, f (R)), introducing new degrees of freedom (e.g., scalar or vector fields), extra dimensions or/and geometric quantities such as torsion and nonmetricity [2, 3]. The hybrid metric-Palatini gravity (HMPG) theory, proposed in [4], is one of such theories. This the*
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