AI 中文总结
该研究通过S矩阵推导霍金辐射，发现黑洞反束缚态构成的量子大气半径约为2.77倍史瓦西半径，其宏观表现为霍金温度下的普通热化气体。
AI 中文摘要
本文通过S矩阵研究标量场在史瓦西黑洞附近的散射。在该框架下，我们通过计算发射率得到霍金辐射的新推导，其给出的玻色-爱因斯坦分布对应的温度为$T_H=(8\pi GM)^{-1}$，即霍金温度。除霍金辐射外，S矩阵还呈现反束缚态，对应势减小（增大）时将成为散射（束缚）态阈值处的激发。我们将这些激发解释为黑洞量子大气的组成部分：事件视界外的热化区域，是霍金辐射的来源。利用反束缚态谱，我们得到大气半径$r_{\text{Atm}} \approx 2.77 r_{s}$，与文献中其他方法得到的结果吻合良好。我们的结果表明，在宏观层面，量子大气表现为处于霍金温度的普通热化气体。
英文摘要
In this paper, we investigate scattering of a scalar field near a Schwarzschild black hole through its $S$-matrix. Within this framework, we obtain a novel derivation of Hawking radiation by computing the emission rate, which yields a Bose--Einstein distribution with temperature $T_H=(8πGM)^{-1}$, the Hawking temperature. In addition to Hawking radiation, the S-matrix exhibits antibound states, corresponding to excitations at the threshold of becoming scattering (bound) states if the potential is decreased (increased). We interpret these excitations as constituents of the black-hole quantum atmosphere: a thermalised region outside of the event horizon, which is the source of the Hawking radiation. Using the spectrum of antibound states, we found the atmospheric radius, $r_{\text{Atm}} \approx 2.77 r_{s}$, which is in good agreement with previous results in the literature obtained through other methods. Our results indicate that, at the macroscopic level, the quantum atmosphere behaves like an ordinary thermalised gas at the Hawking temperature.
Comments10 pages with 01 figure
