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تسجيل مستخدم جديدNon-trivial black hole solutions in $mathit{f(R)}$ gravitational theory
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Recent observation shows that general relativity (GR) is not valid in the strong regime. $mathit{f(R)}$ gravity where $mathit{R}$ is the Ricci scalar, is regarded to be one of good candidates able to cure the anomalies appeared in the conventional general relativity. In this realm, we apply the equation of motions of $mathit{f(R)}$ gravity to a spherically symmetric spacetime with two unknown functions and derive original black hole (BH) solutions without any constrains on the Ricci scalar as well as on the form of $mathit{f(R)}$ gravity. Those solutions depend on a convolution function and are deviating from the Schwarzschild solution of the Einstein GR. These solutions are characterized by the gravitational mass of the system and the convolution function that in the asymptotic form gives extra terms that are responsible to make such BHs different from GR. Also, we show that these extra terms make the singularities of the invariants much weaker than those of the GR BH. We analyze such BHs using the trend of thermodynamics and show their consistency with the well known quantities in thermodynamics like the Hawking radiation, entropy and quasi-local energy. We also show that our BH solutions satisfy the first law of thermodynamics. Moreover, we study the stability analysis using the odd-type mode and shows that all the derived BHs are stable and have radial speed equal to one. Finally, using the geodesic deviations we derive the stability conditions of these BHs.
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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 ${textit F(R)}={textit R}pm{textit 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 ${textit F_1 (R)}=mpfrac{sqrt{textit 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{2Lambda r^2} {3} $ and $h(r)=frac{1}{2}-frac{2M}{r}+frac{q^2}{r^2}-frac{2Lambda r^2} {3} $, respectively. The Ricci scalar of the (A)dS space-times has the form ${textit R}=frac{1+8r^2Lambda}{r^2}$ and the form of ${textit F_1(R)}=mpfrac{textit 2sqrt{R-8Lambda}}{3M}$. 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.
With the successes of $f(R)$ theory as a neutral modification of Einsteins general relativity (GR), we continue our study in this field and attempt to find general natural and charged black hole (BH) solutions. In the previous papers cite{Nashed:2020
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