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arXiv 2101.02205gr-qchep-th
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特殊类F（R）引力理论中非平凡球对称黑洞解的唯一性

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

G. G. L. Nashed

备注：
12 pages, 16 figures
发表信息：
Physics Letters B (2021), Vol. 812, 136012
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摘要：

我们表明，在详细的，唯一的非平凡黑洞（BH）的解决方案，以及中性的带电球对称时空，使用类${\textit F(R)}={\textit R}\pm{\textit F_1 (R)} $，必须有度量的潜力，形式$h(r)=\frac{1}{2}-\frac{2M}{r}$和$h(r)=\frac{1}{2}-\frac{2M}{r}+\frac{q^2}{r^2}$。这些BH具有Ricci标量的非平凡形式，即，$R=\frac{1}{r^2}$和${\textit F_1 (R)}=\mp\frac{\sqrt{\textit R}} {3M} $的形式。对（Anti-）de Sitter，（A）dS，时空重复同样的过程，得到了中性和带电的度规势分别以$h(r)=\frac{1}{2}-\frac{2M}{r}-\frac{2Λr^2} {3} $和$h(r)=\frac{1}{2}-\frac{2M}{r}+\frac{q^2}{r^2}-\frac{2Λr^2} {3} $的形式表示.（A）dS时空的Ricci标量有形式${\textit R}=\frac{1+8r^2Λ}{r^2}$和形式${\textit F_1(R)}=\mp\frac{\textit 2\sqrt{R-8Λ}}{3M}$。我们计算了所有导出的BH的物理量，Hawking温度，熵，准局域能和Gibbs自由能，其行为渐近平坦和（A）dS，并表明它们给出了与文献一致的可接受的物理量。最后，我们证明了热力学第一定律对这些黑洞的有效性。

英文摘要：

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)}=\mp\frac{\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{2Λr^2} {3} $ and $h(r)=\frac{1}{2}-\frac{2M}{r}+\frac{q^2}{r^2}-\frac{2Λr^2} {3} $, respectively. The Ricci scalar of the (A)dS space-times has the form ${\textit R}=\frac{1+8r^2Λ}{r^2}$ and the form of ${\textit F_1(R)}=\mp\frac{\textit 2\sqrt{R-8Λ}}{3M}$. 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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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