论文标题
霍金温度是黑洞外部的总高斯 - 骨网不变
Hawking Temperature as the Total Gauss-Bonnet Invariant of the Region Outside a Black Hole
论文作者
论文摘要
We provide two novel ways to compute the surface gravity ($κ$) and the Hawking temperature $(T_{H})$ of a stationary black hole: in the first method $T_{H}$ is given as the three-volume integral of the Gauss-Bonnet invariant (or the Kretschmann scalar for Ricci-flat metrics) in the total region outside the event horizon;在第二种方法中，它作为riemann张量的表面积分，与事件范围内的杀伤量载体的协变量相关。为了达到黑洞温度（和相关表面重力）的这些新公式，我们首先使用比安奇（Bianchi）身份构建新的差异几何身份和反对称级别-2 $ 2 $张量，对于具有至少一个杀死矢量场的空位有效。高斯 - 骨网张量和高斯标量标量在这种几何身份中起着特殊的作用。我们计算KERR的表面重力和鹰温度和极好的Reissner-Nordström孔作为示例。
We provide two novel ways to compute the surface gravity ($κ$) and the Hawking temperature $(T_{H})$ of a stationary black hole: in the first method $T_{H}$ is given as the three-volume integral of the Gauss-Bonnet invariant (or the Kretschmann scalar for Ricci-flat metrics) in the total region outside the event horizon; in the second method it is given as the surface integral of the Riemann tensor contracted with the covariant derivative of a Killing vector on the event horizon. To arrive at these new formulas for the black hole temperature (and the related surface gravity), we first construct a new differential geometric identity using the Bianchi identity and an antisymmetric rank-$2$ tensor, valid for spacetimes with at least one Killing vector field. The Gauss-Bonnet tensor and the Gauss-Bonnet scalar play a particular role in this geometric identity. We calculate the surface gravity and the Hawking temperature of the Kerr and the extremal Reissner-Nordström holes as examples.
