从有效固有温度探究黑洞量子大气
Investigation of the black-hole quantum atmosphere from the effective proper temperature
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中文总结 AI 辅助
本文基于D维史瓦西黑洞二维径向模型，利用有效固有温度探究黑洞量子大气，发现其大气半径随时空维度增加而减小，大维度下仍保持延伸的外部区域。
中文摘要 AI 辅助
霍金辐射可被视为起源于事件视界处，但其空间起源也可分布在视界外的有限区域。本文利用有效固有温度，在基于D维史瓦西黑洞二维径向部分的易处理模型中探究量子大气。在Hartle--Hawking态下，固有温度由存在霍金辐射共形反常时的热力学第一定律推导得出；在Unruh态下，我们将固有温度分解为两个手性温度，分别对应入射通量的T_L和出射通量的T_R。通过证明T_R是表征出射霍金通量的有效固有温度，并结合Hartle--Hawking态下的固有温度，我们将大气半径有效定义为有效固有温度达到最大值的径向位置。随后，我们针对不同时空维度数值计算量子大气的大气半径，结果表明其随时空维度数增加而单调减小；在大维度极限下，我们发现大气半径与视界之间仍保持有限径向因子的间隔，这说明量子大气在任意维度下都可作为延伸的外部区域存在。
英文摘要
Hawking radiation may be regarded as originating at the event horizon; however, its spatial origin can instead be distributed over a finite region outside the horizon. In this paper, using an effective proper temperature, we investigate the quantum atmosphere within a tractable model based on the two-dimensional radial sector of $D$-dimensional Schwarzschild black holes. In the Hartle--Hawking state, the proper temperature is derived from the first law of thermodynamics in the presence of the conformal anomaly associated with Hawking radiation. In the Unruh state, we decompose the proper temperature into two chiral temperatures, $T_{\rm L}$ and $T_{\rm R}$, associated with the ingoing and outgoing fluxes, respectively. Demonstrating $T_{\rm R}$ as the effective proper temperature characterizing the outgoing Hawking flux with the proper temperature in the Hartle-Hawking state, we define the atmospheric radius effectively as the radial position at which the effective proper temperature attains its maximum. We then numerically compute the atmospheric radius of the quantum atmosphere for various spacetime dimensions and show that it decreases monotonically as the number of spacetime dimensions increases. In the large-dimensional limit, we find that the atmospheric radius remains separated from the horizon by a finite radial factor, indicating that the quantum atmosphere can persist as an extended exterior region in any dimension.
