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arXiv 2007.02224gr-qc
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超自旋的Kerr-Sen-AdS $_4$黑洞总是超熵的吗?

Are ultra-spinning Kerr-Sen-AdS$_4$ black holes always super-entropic ?

Di Wu, Puxun Wu, Hongwei Yu, Shuang-Qing Wu

摘要:

研究了四维Kerr-Sen-AdS黑洞及其超自旋黑洞的热力学性质,证明了两个黑洞都满足黑洞热力学第一定律和Bekenstein-Smarr质量公式.此外,我们推导出新的Christodoulou-Ruffini式的平方质量公式,通常和超自旋的Kerr-Sen-AdS $_4$解决方案。我们表明,这种超自旋克尔森AdS $_4$黑洞并不总是违反反向等周不等式(RII),因为等周比的值可以大于/小于,或等于单位,这取决于在参数空间中的解决方案参数。这一性质与Kerr-Newman-AdS $_4$超熵黑洞严格违反RII的性质明显不同,尽管两者在视界几何和共形边界等方面有相似之处.此外,还发现极端超自旋Kerr-Sen-AdS $_4$黑洞和极端超熵Kerr-Newman-AdS $_4$黑洞存在相同的质量下界($m_e \geqslant 8l/\sqrt{27}$,其中$l$为宇宙学尺度),但前者有一个最大视界半径:$r_{\rm\, HP} = l/\sqrt{3}$,它是后者的最小值.因此,这两种不同的四维超自旋带电AdS黑洞表现出一些显著的物理差异。

英文摘要:

We study thermodynamics of the four-dimensional Kerr-Sen-AdS black hole and its ultra-spinning counterpart, and verify that both black holes fullfil the first law and Bekenstein-Smarr mass formulae of black hole thermodynamics. Furthermore, we derive new Christodoulou-Ruffini-like squared-mass formulae for the usual and ultra-spinning Kerr-Sen-AdS$_4$ solutions. We show that this ultra-spinning Kerr-Sen-AdS$_4$ black hole does not always violate the Reverse Isoperimetric Inequality (RII) since the value of the isoperimetric ratio can be larger/smaller than, or equal to unity, depending upon where the solution parameters lie in the parameters space. This property is obviously different from that of the Kerr-Newman-AdS$_4$ super-entropic black hole, which always strictly violates the RII, although both of them have some similar properties in other aspects, such as horizon geometry and conformal boundary. In addition, it is found that while there exists the same lower bound on mass ($m_e \geqslant 8l/\sqrt{27}$ with $l$ being the cosmological scale) both for the extremal ultra-spinning Kerr-Sen-AdS$_4$ black hole and for the extremal super-entropic Kerr-Newman-AdS$_4$ case, the former has a maximal horizon radius: $r_{\rm\, HP} = l/\sqrt{3}$ which is the minimum of the latter. Therefore, these two different kinds of four-dimensional ultra-spinning charged AdS black holes exhibit some significant physical differences .

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