论文标题
2+1维度的旋转黑洞的体积
Volume of a rotating black hole in 2+1 dimensions
论文作者
论文摘要
在本文中，我们将该技术应用于Christodoulou和Rovelli为Schwarzild Blackhole开发的黑洞的最大体积估计以及Zhang等人的非旋转BTZ Black Hole，以在2+1个尺寸的旋转黑洞中。我们使用Christodoulou和Rovelli展示的Lagrangian配方来得出旋转BTZ黑孔的最大超表面方程。此外，我们使用Bengtsson等人先前说明的Kerr Black Hole的最大化技术来得出我们案件的类似结果。我们认为，对高表面的体积的最大贡献来自我们所谓的稳态半径，我们显示的取决于质量M和ADS长度尺度。我们证明，可以使用独立考虑消失外部曲率的独立考虑来达到这种稳态半径。我们表明，最大超表面的这一段的体积，Cr体积取决于质量，ADS长度尺度和角动量J。我们进一步计算了近极黑孔上的标量场的熵。
In this article we apply the technique for maximal volume estimation of a black hole developed by Christodoulou and Rovelli for Schwarzchild blackhole and by Zhang et al for non rotating BTZ black hole, to the case of a rotating black hole in 2+1 dimensions. We derive the equation of the maximal hypersurface for the rotating BTZ blackhole using the Lagrangian formulation demonstrated by Christodoulou and Rovelli . Further we use maximization technique illustrated earlier by Bengtsson et al for Kerr black hole to arrive at the similar result for our case. We argue that the maximum contribution to the volume of the hypersurface comes from what we call the steady state radius, which we show depends on mass M and the AdS length scale. We demonstrate that this steady state radius can be arrived at using independent considerations of vanishing extrinsic curvature. We show that the volume of this segment of the maximal hypersurface, the CR volume, depends on mass, AdS length scale and angular momentum J. We further compute the entropy of a scalar field living on the maximal hypersurface for a near extremal black hole and show that it is proportional to the horizon entropy of the black hole.
