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

Alexandre Arbey (1, 2) , Jérémy Auffinger (1) , Marc Geiller (3) , Etera R. Livine (3) , Francesco Sartini (3)

1 IP2I Lyon - Institut de Physique des 2 Infinis de Lyon
2 IUF - Institut universitaire de France
3 ENS de Lyon - École normale supérieure de Lyon

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 quasinormal 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–Nordström) 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.

Mots clés: General relativity; alternative theories of gravity; radiation: Hawking; black hole: static; black hole: higher-dimensional; black hole: stability; black hole: charge; spin: 1/2; spin: 0; spin: 1; spin: 2; metric: Schwarzschild; quantum gravity: loop space; Teukolsky equation; Reissner-Nordstroem; gravitation; symmetry: rotation; gravitation: model; field theory: massless; quasinormal mode; quantization: polymer

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Alexandre Arbey, Jérémy Auffinger, Marc Geiller, Etera R. Livine, Francesco Sartini. Hawking radiation by spherically-symmetric static black holes for all spins: Teukolsky equations and potentials. Physical Review D, 2021, 103 (10), pp.104010. ⟨10.1103/PhysRevD.103.104010⟩. ⟨hal-03129542⟩