One-loop Quantum Gravity in Schwarzschild Spacetime

TL;DR

This paper develops a quantum theory for linearized gravitational perturbations around a Schwarzschild black hole, analyzing expectation values of key operators in different quantum states.

Contribution

It introduces a framework using perturbed Weyl scalars and computes expectation values in various quantum states, advancing understanding of quantum effects in black hole spacetimes.

Findings

Expectation values of perturbed Weyl scalars are computed for different states.

Differences in expectation values between states are numerically evaluated.

Provides a basis for understanding quantum gravitational effects near black holes.

Abstract

The quantum theory of linearized perturbations of the gravitational field of a Schwarzschild black hole is presented. The fundamental operators are seen to be the perturbed Weyl scalars $\dot\Psi_0$ and $\dot\Psi_4$ associated with the Newman-Penrose description of the classical theory. Formulae are obtained for the expectation values of the modulus squared of these operators in the Boulware, Unruh and Hartle-Hawking quantum states. Differences between the renormalized expectation values of both $\bigl| \dot\Psi_0 \bigr|^2$ and $\bigl| \dot\Psi_4 \bigr|^2$ in the three quantum states are evaluated numerically.