Metric Reconstruction for Generic Black-Hole Perturbations

TL;DR

This paper introduces a traceful radiation gauge method for metric reconstruction in Petrov type D spacetimes, enabling inclusion of generic sources like matter shells.

Contribution

It develops a new traceful radiation gauge approach that overcomes previous limitations, allowing for metric reconstruction with generic sources in black hole perturbations.

Findings

Successfully reconstructs metric for Schwarzschild with a static shell

Derives transport equations for metric trace from stress-energy tensor

Hierarchically determines remaining metric components from Newman-Penrose equations

Abstract

Standard (radiation-gauge) metric reconstruction excludes generic sources because it requires a tracefree metric perturbation. We remove this obstruction for perturbations of Petrov type D spacetimes by introducing a traceful radiation gauge. Two first-order transport equations determine the metric trace from the stress-energy tensor, and the remaining metric components follow hierarchically from the Newman-Penrose equations. We illustrate the method for a Schwarzschild black hole with a thin static shell, including a source-supported static completion sector.