论文标题
从指数校正到黑洞熵的量子几何形状的签名
Signatures of quantum geometry from exponential corrections to the black hole entropy
论文作者
论文摘要
最近在[Phys。莱特牧师。 125（2020）041302]在黑洞的$ \ exp（-a/4l_p^2）$（-a/4l_p^2）$中，在黑洞入口的Bekenstein-Hawking形式中，对固定在黑洞地平线上的量子状态进行了微晶体计数。在本文中，我们开发了一种新颖的方法，以从黑洞的熵中获取时空几何形状的可能形式，以达到给定的地平线半径。还讨论了该解决方案对于给定能量量张量的独特性。值得注意的是，重建的黑洞几何形状与非交流启发的Schwarzschild黑洞具有惊人的相似性[Phys。 Lett。 B 632（2006）547]。我们还使用爱因斯坦磁场方程来获得物质密度函数，以从黑洞的热力学重建我们重建的几何形状。这些也与非共同启发的Schwarzschild黑洞的物质密度函数相似。简要讨论了公制的共形结构，并绘制了penrose-carter图。然后，我们计算有效黑洞几何形状的科马尔能量和Smarr公式，并将其与非交流启发的Schwarzschild黑洞进行比较。我们还讨论了解决方案的一些天体物理含义。最后，我们提出了一组量子爱因斯坦真空场方程，作为一种解决方案，我们获得了这项工作中获得的时空溶液之一。然后，我们显示了爱因斯坦真空场方程与黑洞热力学的第一定律之间的直接连接。
It has been recently shown in [Phys. Rev. Lett. 125 (2020) 041302] that microstate counting carried out for quantum states residing on the horizon of a black hole leads to a correction of the form $\exp(-A/4l_p^2)$ in the Bekenstein-Hawking form of the black hole entropy. In this paper, we develop a novel approach to obtain the possible form of the spacetime geometry from the entropy of the black hole for a given horizon radius. The uniqueness of this solution for a given energy-momentum tensor has also been discussed. Remarkably, the black hole geometry reconstructed has striking similarities to that of noncommutative-inspired Schwarzschild black holes [Phys. Lett. B 632 (2006) 547]. We also obtain the matter density functions using Einstein field equations for the geometries we reconstruct from the thermodynamics of black holes. These also have similarities to that of the matter density function of a noncommutative-inspired Schwarzschild black hole. The conformal structure of the metric is briefly discussed and the Penrose-Carter diagram is drawn. We then compute the Komar energy and the Smarr formula for the effective black hole geometry and compare it with that of the noncommutative-inspired Schwarzschild black hole. We also discuss some astrophysical implications of the solutions. Finally, we propose a set of quantum Einstein vacuum field equations, as a solution of which we obtain one of the spacetime solutions obtained in this work. We then show a direct connection between the quantum Einstein vacuum field equations and the first law of black hole thermodynamics.
