Canonical quantization and black hole perturbations

TL;DR

This paper explores a potential approach to quantize linearized gravity around black holes using the Teukolsky equation, revealing that the resulting gravitons are inherently unstable.

Contribution

It introduces a quadratic Lagrangian for the Teukolsky equation and discusses the instability of gravitons bound to Kerr black holes.

Findings

Elementary excitations are unstable.

A simple quadratic Lagrangian for the Teukolsky equation is proposed.

Implications for quantum gravity near black holes.

Abstract

We examine the possibility of a constraint-free quantization of linearized gravity, based on the Teukolsky equation for black hole perturbations. We exhibit a simple quadratic (but complex) Lagrangian for the Teukolsky equation, leading to the interpretation that the elementary excitations (gravitons bound to the Kerr black hole) are unstable.