Gravitational Perturbations of a Radiating Spacetime

TL;DR

This paper develops a theoretical framework for analyzing gravitational perturbations in radiating spacetimes, deriving separable equations and obtaining analytic solutions for specific models like the Vaidya spacetime.

Contribution

It introduces a new approach to derive and solve perturbation equations for radiating black hole spacetimes, including the Vaidya metric, with analytic solutions for the Hiscock linear mass model.

Findings

Perturbation equations are derived for radiating spacetimes.

Equations are separable for the Hiscock linear mass model.

Analytic solutions are obtained and characterized.

Abstract

This paper discusses the problem of gravitational perturbations of radiating spacetimes. We lay out the theoretical framework for describing the interaction of external gravitational fields with a radiating spacetime. This is done by deriving the field perturbation equations for a radiating metric. The equations are then specialized to a Vaidya spacetime. For the Hiscock ansatz of a linear mass model of a radiating blackhole the equations are found separable. Further, the resulting ordinary differential equations are found to admit analytic solutions. We obtain the solutions and discuss their characteristics.