Uniqueness of non-trivial spherically symmetric black hole solution in special classes of F(R) gravitational theory

Abstract

We show, in detail, that the only non-trivial black hole (BH) solutions for a neutral as well as a charged spherically symmetric space-times, using the class $\text{F}(R)=\text{R}\pm {\text{F}}_1(R)$, must-have metric potentials in the form $h(r)=\frac{1}{2}-\frac{2M}{r}$ and $h(r)=\frac{1}{2}-\frac{2M}{r}+\frac{q^2}{r^2}$. These BHs have a non-trivial form of Ricci scalar, i.e., $R=\frac{1}{r^2}$ and the form of ${\text{F}}_1(R)=\mp \frac{\sqrt{\text{R}}}{3M}$. We repeat the same procedure for (Anti-)de Sitter, (A)dS, space-time and got the metric potentials of neutral as well as charged in the form $h(r)=\frac{1}{2}-\frac{2M}{r}-\frac{2\Lambda r^2}{3}$ and $h(r)=\frac{1}{2}-\frac{2M}{r}+\frac{q^2}{r^2}-\frac{2\Lambda r^2}{3}$, respectively. The Ricci scalar of the (A)dS space-times has the form $\text{R}=\frac{1+8r^2\Lambda }{r^2}$ and the form of ${\text{F}}_1(R)=\mp \frac{\text{2}\sqrt{R-8\Lambda }}{3M}$. We calculate the thermodynamical quantities, Hawking temperature, entropy, quasi-local energy, and Gibbs-free energy for all the derived BHs, that behaves asymptotically as flat and (A)dS, and show that they give acceptable physical thermodynamical quantities consistent with the literature. Finally, we prove the validity of the first law of thermodynamics for those BHs.

12 pages, 16 figures

References in corpus (16)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• Static spherically symmetric perfect fluid solutions in $f(R)$ theories of gravity
• Cosmological Constraints on f(R) Acceleration Models
• Higher dimensional charged $f(R)$ black holes
• Thermodynamics of apparent horizon and modified Friedman equations
• Four-dimensional black holes in Einsteinian cubic gravity
• Charged spherically symmetric black holes in $f(R)$ gravity and their stability analysis
• Thermodynamics of higher dimensional topological charged AdS black branes in dilaton gravity
• On the Energy Issue for a Class of Modified Higher Order Gravity Black Hole Solutions
• 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

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