Charged spherically symmetric black holes in $f(R)$ gravity and their stability analysis
| Autor: | Nashed, Gamal G. L., Capozziello, Salvatore |
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| Rok vydání: | 2019 |
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| Zdroj: | Phys. Rev. D 99, 104018 (2019) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.99.104018 |
| Popis: | A new class of analytic charged spherically symmetric black hole solutions, which behave asymptotically as flat or (A)dS spacetimes, is derived for specific classes of $f(R)$ gravity, i.e., $f(R)=R-2\alpha\sqrt{R}$ and $f(R)=R-2\alpha\sqrt{R-8\Lambda}$, where $\Lambda$ is the cosmological constant. These black holes are characterized by the dimensional parameter $\alpha$ that makes solutions deviate from the standard solutions of general relativity. The Kretschmann scalar and squared Ricci tensor are shown to depend on the parameter $\alpha$ which is not allowed to be zero. Thermodynamical quantities, like entropy, Hawking temperature, quasi-local energy and the Gibbs free energy are calculated. From these calculations, it is possible to put a constrain on the dimensional parameter $\alpha$ to have $0<\alpha<0.5$, so that all thermodynamical quantities have a physical meaning. The interesting result of these calculations is the possibility of a negative black hole entropy. Furthermore, present calculations show that for negative energy, particles inside a black hole, behave as if they have a negative entropy. This fact gives rise to instability for $f_{RR}<0$. Finally, we study the linear metric perturbations of the derived black hole solution. We show that for the odd-type modes, our black hole is always stable and has a radial speed with fixed value equal to $1$. We also, use the geodesic deviation to derive further stability conditions. Comment: 17 pages, 5 figures, accepted for publication in Physical Review D. This version contains an Addendum where a typo is pointed out. arXiv admin note: text overlap with arXiv:1107.3705 by other authors |
| Databáze: | arXiv |
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