(2 + 1)-Dimensional Solutions in F(R) Gravity

Abstract

Motivated by the well-known charged BTZ black holes, we look for (2 + 1)-dimensional solutions of F (R) gravity. At first we investigate some near horizon solutions and after that we obtain asymptotically Lifshitz black hole solutions. Finally, we discuss about rotating black holes with exponential form of F (R) theory. I. INTRODUCTIONRegardless of the dark energy nature, one of the most popular ad hoc theories to explain the current accelerated expansion of our universe is dark energy [1]. Necessity of dark energy comes from the fact that we need to have a negative pressure (repulsive action) to interpret cosmic expansion. Since the determination of dark energy nature is an important challenge for the physics communities, it is inevitable to look for an alternative theories scenario for dark energy to address the observational evidences. Modified gravity theory, instead of general relativity, is an alternative plan to describe the late time acceleration [2].In recent years, variety of Modified theories of classical gravity have been proposed to solve some puzzles of standard general relativity. Amongst them the well-known F (R) theory, whose Lagrangian density is an arbitrary function of the Ricci scalar, is quite special and received a growing attention (see for example [3] and references therein). F (R) gravity provides a technically powerful tool to deal with the early time inflation [4], late time acceleration [5], the hierarchy and singularity problems [6,7] and (the nature of) dark energy [8]. Holographic superconductor with linear and nonlinear Maxwell field in the frame of modified gravity has been studied [9, 10] and the condensation effects of nonlinearity in Maxwell field and curvature terms have been investigated in [10]. Although, the field equations of F (R) theories are of four-order and solving them, directly, is so complicated, their valuable consequences motivate us to consider them and investigate their interesting properties. Using a suitable conformal transformation, it has been shown that F (R) gravity models are equivalent to classical Einstein's gravity with an extra scalar field. Also, we can apply some limitations on the model parameters to guarantee that the model follows the stability condition (the scalaron is not a tachyon) and has no ghosts [11,12]. Some viable models of F (R) theories have been widely investigated in the literature over the past few years [12][13][14][15][16][17][18].In addition to the F (R) theories, one of the interesting subjects for recent study is the investigation of three dimensional black holes [19]. Considering three dimensional spacetimes helps us to find some conceptual issues in the black hole properties, quantum view of gravity and string theory [20,21]. Therefore, theoretical physicists have an interest in the (2 + 1)-dimensional manifolds and their properties [22]. Moreover, three dimensional solutions perform an essential role to improve our comprehension of gravitational interaction in low dimensional manifolds [23]. In addition, it is interesting...

Asymptotically charged BTZ black holes in gravity’s rainbow

“…For more subjects related to BTZ solutions, we refer the reader to Refs. [61][62][63][64][65][66][67][68][69][70][71][72] and references therein.…”

Thin-shell wormholes in $$(2+1)$$-dimensional F(R) theories

“…The only non-null independent component of the electromagnetic field is F tr = Q/r 2 . When Q = 0, the well-known vacuum static BTZ geometry [54,55] of General Relativity is obtained, which is also a solution in F(R) gravity [68] with constant scalar curvature. The spacetime is asymptotically anti-de Sitter since it requires that R 0 < 0.…”

“…Thin shells of matter [61] as well as thin-shell wormholes [62][63][64][65][66] were also widely examined. Black hole solutions with (2 + 1) dimensions in F(R) gravity have been found [67][68][69][70]. In the recent article [71], thin shells of matter in (2 + 1) dimensions within F(R) theory have been analyzed in detail and examples of stable configurations under radial perturbations have been found.…”

Exact charged black hole solutions in D-dimensions in f(R) gravity

“…In (2 + 1)-dimensions, near horizon solutions, asymptotically Lifshitz black hole solutions and rotating black holes with exponential form of f (R) theory have been discussed in [40]. They first gave the basic field equations as same as our equations with D = 3, but their solution is different with our solution.…”