论文标题
电荷对BTZ黑洞内部体积的影响
Effects of charge on the interior volume of BTZ black holes
论文作者
论文摘要
在本文中，我们将克里斯托杜卢和罗维利（CR）开发的黑洞的最大体积估计扩展到了2+1个维度的带电BTZ黑洞的情况。该技术涉及对假设粒子在时空变量定义的辅助歧管中运动的运动方程的研究。然后，我们将该估计值与使用最大化方法和外部曲率方法计算的体积进行比较。黑洞的电荷q在度量标准中显示为对数项，因此不存在该体积的分析解决方案。因此，首先，当电荷Q非常小时，即Q << 1，然后进行数值分析以求解音量以获取电荷的更通用值时，我们将计算稳态半径和限制情况的体积。我们发现该音量随着时间的推移而单调增长。我们进一步研究了生活在近极黑洞最大超表面上的无质量标量场熵的功能行为。我们表明，与地平线熵相比，该体积熵表现出非常不同的功能形式。
In this article we extend the variational technique for maximal volume estimation of a black hole developed by Christodoulou and Rovelli (CR) to the case of a charged BTZ black hole in 2+1 dimensions. The technique involves a study of the equation of motion of a hypothetical particle moving in an auxiliary manifold defined by spacetime variables. We then compare this estimation with the volume computed using maximization method and extrinsic curvature method. The charge Q of the black hole appears as a log term in the metric and hence an analytical solution for the volume does not exist. So first we compute the steady state radius and the volume for limiting case when the charge Q is very small i.e. Q << 1 and then carry out a numerical analysis to solve for the volume for more generic values of the charge. We find that the volume grows monotonically with the advance time. We further investigate the functional behaviour of the entropy of a massless scalar field living on the maximal hypersurface of a near extremal black hole. We show that this volume entropy exhibits a very different functional form compared to the horizon entropy.
