Hawking radiation by spherically-symmetric static black holes for all spins: I -- Teukolsky equations and potentials

TL;DR

This paper derives Teukolsky equations and potentials for all spins in spherically symmetric static black holes, enabling analysis of Hawking radiation and quasi-normal modes across various black hole types, including quantum gravity inspired models.

Contribution

It provides the first comprehensive derivation of Teukolsky equations and potentials for all spins in general spherically symmetric static metrics, extending previous work to new black hole solutions.

Findings

Derived Teukolsky equations for all spins in static black holes.

Computed radial potentials for spin 1 and 1/2 fields.

Applied formulas to various black hole metrics, including charged and quantum gravity models.

Abstract

In the context of the dynamics and stability of black holes in modified theories of gravity, we derive the Teukolsky equations for massless fields of all spins in general spherically-symmetric and static metrics. We then compute the short-ranged potentials associated with the radial dynamics of spin 1 and spin 1/2 fields, thereby completing the existing literature on spin 0 and 2. These potentials are crucial for the computation of Hawking radiation and quasi-normal modes emitted by black holes. In addition to the Schwarzschild metric, we apply these results and give the explicit formulas for the radial potentials in the case of charged (Reissner--Nordstr\"om) black holes, higher-dimensional black holes, and polymerized black holes arising from loop quantum gravity. These results are in particular relevant and applicable to a large class of regular black hole metrics. The phenomenological applications of these formulas will be the subject of a companion paper.