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 $$f(R) = R -2\alpha \sqrt{R}$$ f ( R ) = R - 2 α R and derive an exact black hole solution. Then, we consider the asymptotically (A)dS model $$f(R) =R -2 \Lambda -2 \alpha \sqrt{R-4 \Lambda }$$ f ( R ) = R - 2 Λ - 2 α R - 4 Λ and derive an exact black hole solution. In both cases the modified gravity parameter $$\alpha $$ α , which has the dimension of the inverse mass, 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.

Astrophysical and electromagnetic emissivity properties of black holes surrounded by a quintessence type exotic fluid in the Scalar-Vector-Tensor Modified Gravity

“…where T q µν stands for the quintessence part [18], and T V µν describes the vector field [42]. For the derivation of the metric one can find more details in [47][48][49] as well.…”

Black Holes with Electric and Magnetic Charges in F(R)$F(R)$ Gravity

“…Thus, it is important to investigate the stationary black hole solutions in the $$F(R)$$ gravity coupled with the electromagnetic fields and the contribution from the electromagnetic fields to the geometry in the framework of the $$F(R)$$ gravity. The black hole solutions in $$F(R)$$ gravity in vacuum or in the case with electromagnetic fields have been studied in [30, 31, 38, 39, 44–50] and in [51–53], the scalar fields have been included as matter in three and four dimensions while the $$F(R)$$ gravity coupled with/without non‐minimally coupled scalar fields as a matter has been studied in the frame of cosmology. [ 54,55 ] Capozziello et al.…”

Thin-shell wormholes in $N$-dimensional $F(R)$ gravity

“…Due to their relative simplicity, one of the most popular among them are the F(R) theories [1][2][3], which introduce a modification in the general relativity action by replacing the Ricci scalar R by a function F (R). Many solutions in four dimensions have been found in this theory: among them, traversable wormholes [4][5][6][7][8] and spherically symmetric black holes [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Additional solutions have been explored in higher dimensions [23][24][25][26] as well as in lower ones [27].…”