Hawking Temperatures of Dynamical Black Holes from the RVB--Residue Method:Vaidya and Kinnersley Geometries
Abstract
This paper develops a local residue-based extension of the Robson--Villari--Biancalana method for calculating Hawking temperatures of dynamical black holes. Since non-stationary black holes generally do not admit a global timelike Killing vector, their temperature must be understood in a local, near-horizon, and quasi-stationary sense. By analytically continuing the near-horizon radial function into the complex plane, the Hawking temperature can be extracted from the residue of the inverse horizon function at the simple pole corresponding to the local horizon. This residue prescription is first applied to the Vaidya black hole, where it reproduces the standard local trapping-horizon temperature (T=1/(8πM(v))). The method is then extended to the arbitrarily accelerating Kinnersley black hole, whose horizon depends on time and angular coordinates. In this case, the RVB--residue method yields a point-dependent local Hawking temperature consistent with the generalized tortoise-coordinate approach. The results show that the RVB--residue method can be naturally generalized from stationary black holes to dynamical and non-spherical black holes, provided that the temperature is interpreted as a local near-horizon quantity rather than a global equilibrium temperature.
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BibTeX
@misc{chen2026hawking,
title = {{Hawking Temperatures of Dynamical Black Holes from the RVB--Residue Method:Vaidya and Kinnersley Geometries}},
author = {Wen-Xiang Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.10220},
eprint = {2606.10220},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.10220},
}
RIS
TY - UNPB
TI - Hawking Temperatures of Dynamical Black Holes from the RVB--Residue Method:Vaidya and Kinnersley Geometries
AU - Wen-Xiang Chen
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2606.10220
UR - https://arxiv.org/abs/2606.10220
AB - This paper develops a local residue-based extension of the Robson--Villari--Biancalana method for calculating Hawking temperatures of dynamical black holes. Since non-stationary black holes generally do not admit a global timelike Killing vector, their temperature must be understood in a local, near-horizon, and quasi-stationary sense. By analytically continuing the near-horizon radial function into the complex plane, the Hawking temperature can be extracted from the residue of the inverse horizon function at the simple pole corresponding to the local horizon. This residue prescription is first applied to the Vaidya black hole, where it reproduces the standard local trapping-horizon temperature (T=1/(8πM(v))). The method is then extended to the arbitrarily accelerating Kinnersley black hole, whose horizon depends on time and angular coordinates. In this case, the RVB--residue method yields a point-dependent local Hawking temperature consistent with the generalized tortoise-coordinate approach. The results show that the RVB--residue method can be naturally generalized from stationary black holes to dynamical and non-spherical black holes, provided that the temperature is interpreted as a local near-horizon quantity rather than a global equilibrium temperature.
ER -