近日，印度理工学院Bibhas Ranjan Majhi团队研究了二维黑洞的热标量场应力张量及其近视界性质。该项研究成果发表在2025年10月21日出版的《高能物理杂志》上。
研究组计算了在（1 + 1）维静态黑洞时空上无质量标量场的热重整化能动张量分量，该分量导致了迹反常。利用这些分量，分别评估了静态观测者和自由落体观测者观测到的能量密度与能流。有趣的是，当标量场与黑洞视界温度（由霍金公式给出）处于热平衡状态时，对于Unruh和Boulware热态而言，这两类观测者在视界处观测到的上述物理量均具有有限值。
而在Hartle-Hawking热态中，无论场温度取值如何，两类观测者在视界处观测到的能量密度与能流始终有限。特别地，在史瓦西时空情形中，初始速度为零的自由落体观测者，其初始临界位置为rci= (3/2)rH（其中rH为视界半径），在该位置处观测到的能量密度为零。
附：英文原文
Title: Thermal scalar field stress tensor on a two dimensional black hole and its near horizon properties
Author: Samanta, Saurav, Majhi, Bibhas Ranjan
Issue&Volume: 2025-10-21
Abstract: We calculate the thermal renormalized energy-momentum tensor components of a massless scalar field, leading to trace anomaly, on a (1 + 1) dimensional static black hole spacetime. Using these, the energy density and flux, seen by both static and freely-falling observers, are evaluated. Interestingly for both these observers the aforementioned quantities in the thermal version of Unruh and Boulware states are finite at the horizon when the scalar field is in thermal equilibrium with the horizon temperature (given by the Hawking expression). Whereas in Hartle-Hawking thermal state both the observers see finite energy-density and flux at the horizon, irrespective of the value of field temperature. Particularly in the case of Schwarzschild spacetime a freely falling observer, starts with initial zero velocity, finds its initial critical position rci= (3/2)rH, where rH is the horizon radius for which energy-density vanishes.
DOI: 10.1007/JHEP10(2025)183
Source: https://link.springer.com/article/10.1007/JHEP10(2025)183