Exact Black Hole Solutions with a Conformally Coupled Scalar Field and Dynamic Ricci Curvature in $f(R)$ Gravity Theories

Abstract

We report exact black hole solutions in asymptotically flat or (A)dS four-dimensional spacetime with a conformally coupled self-interacting scalar field in f (R) gravity. We first consider the asymptotically flat model f (R) = R − 2α √ R and derive an exact black hole solution. Then, we consider the asymptotically (A)dS modeland derive an exact black hole solution. In both cases the modified gravity parameter α cannot be set to zero and the self-interacting potential is determined from the Klein-Gordon equation, preserving the conformal invariance. The thermodynamics of the solutions is also studied.

$(2+1)$-Dimensional Black Holes in $f(R,ϕ)$ Gravity

“…We also plot the horizon radius as a function of α. The fact that the larger the deviation from the GR solution [4] is, the smaller the horizon radius becomes, is in agreement with the (3 + 1)-dimensional case [64]. Next, we will briefly discuss scalar perturbations of the obtained spacetime.…”

“…The Klein-Gordon equation can be obtained by taking the covariant derivative of Einstein's equation [64]. Therefore, we have a system of three independent equations with four unknown functions: the f (R) function, the potential V (φ), the scalar field φ(r) and the metric function b(r).…”

“…Static and spherically symmetric black hole solutions were investigated with constant curvature, with and without electric charge and cosmological constant in [59][60][61]. Scalar fields have been recently introduced as matter fields in the context of f (R), exact black hole solutions have been found and the corresponding physical properties have been investigated in [63][64][65], while the stability of f (R) black holes was also considered in [66]. The possibility of dressing the black hole with a gravitational hair has also been discussed in [67,68].…”

$f({\sf R})$ Gravity Wormholes sourced by a Phantom Scalar Field

“…Black holes in f (R) gravity theories with constant and non-constant Ricci curvature in vaccum or coupled to electrodynamics have been found [32]- [45] while in [46][47][48] scalar fields are introduced as matter in (2 + 1) and (3 + 1)-dimensional f (R) gravity and the corresponding black hole solutions are investigated. This particular type of theory, f (R) gravity and non-minimally coupled scalar fields as matter has been previously considered for cosmological purposes [49,50].…”