Spherically symmetric black holes in f ( R ) gravity: is geometric scalar hair supported?

Abstract

We critically discuss current research on black hole (BH) solutions in f (R) gravity and shed light on its geometrical and physical significance. We also investigate the meaning, existence or lack thereof of Birkhoff's theorem (BT) in this kind of modified gravity. We then focus on the analysis and search for non-trivial (i.e. hairy) asymptotically flat (AF) BH solutions in static and spherically symmetric (SSS) spacetimes in vacuum having the property that the Ricci scalar does not vanish identically in the domain of outer communication.To do so, we provide and enforce regularity conditions at the horizon in order to prevent the presence of singular solutions there. Specifically, we consider several classes of f (R) models like those proposed recently for explaining the accelerated expansion in the Universe and which have been thoroughly tested in several physical scenarios. Finally, we report analytical and numerical evidence about the absence of geometric hair in AFSSSBH solutions in those f (R) models. First, we submit the models to the available no-hair theorems (NHTs), and in the cases where the theorems apply, the absence of hair is demonstrated analytically. In the cases where the theorems do not apply, we resort to a numerical analysis due to the complexity of the non-linear differential equations. With that aim, a code to solve the equations numerically was built and tested using well-known exact solutions. In a future investigation we plan to analyze the problem of hair in de Sitter and anti-de Sitter backgrounds.

Anisotropic solutions by gravitational decoupling

“…Indeed, this simple and systematic method could be conveniently exploited in a large number of relevant cases, such as the Einstein-Maxwell [20] and Einstein-Klein-Gordon system [21][22][23][24], for higher derivative gravity [25][26][27], f (R)-theories of gravity [28][29][30][31][32][33][34], Hořava-aether gravity [35,36], polytropic spheres [37][38][39], among many others. In this respect, the simplest practical application of the MGD-decoupling consists in extending known isotropic and physically acceptable interior solutions for spherically symmetric self-gravitating systems into the anisotropic domain, at the same time preserving physical acceptability, which represents a highly non-trivial problem [40] (for obtaining anisotropic solutions in a generic way, see for instance Refs.…”

Spherically symmetric black holes with electric and magnetic charge in extended gravity: physical properties, causal structure, and stability analysis in Einstein’s and Jordan’s frames

“…related to this, a numerous of research papers have been focused on the study of black hole solutions, as e.g. [5][6][7][8][9][10][11][12][13][14], and neutron stars solutions [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. We should note that f (R) theories can be related with theories of Brans-Dicke type (see, e.g., [29]), in particular with the ones involving a scalar and a potential of gravitational origin [30,31].…”

“…The same theorem forbids the existence of hairy black hole solutions in the case of the R 2 model [6,7,12,13]. Several black holes have been got already for f (R) theories [6,[34][35][36][37][38][39][40][41][42][43][44]. And their physical properties are discussed in, e.g., [45][46][47][48].…”

Using MGD Gravitational Decoupling to Extend the Isotropic Solutions of Einstein Equations to the Anisotropical Domain

“…In consequence we are able to find analytical internal solutions of Einstein equations that considers an energy‐momentum tensor of the form where α is a coupling constant and is a gravitational source. In fact, with this approach we are able to study different systems as polytropic spheres, Horava‐aether gravity, Einstein‐Maxwell, Einstein Klein‐Gordon, and many others (see for example []).…”