Semi-analytical approach for the Vaidya metric in double-null coordinates

TL;DR

This paper introduces a semi-analytical method to analyze the Vaidya metric in double-null coordinates for general mass functions, providing new insights and an analytical solution for a specific mass function.

Contribution

The paper develops a semi-analytical approach to study the Vaidya metric with arbitrary mass functions in double-null coordinates, including a new analytical solution for a (1/v)-mass function.

Findings

Method enables qualitative and quantitative analysis of the Vaidya metric.

New analytical solution for the (1/v)-mass function.

Applicable to generic mass functions beyond constant, linear, or exponential cases.

Abstract

We reexamine here a problem considered in detail before by Waugh and Lake: the solutions of spherically symmetric Einstein's equations with a radial flow of unpolarized radiation (the Vaidya metric) in double-null coordinates. This problem is known to be not analytically solvable, the only known explicit solutions correspond to the constant mass case (Schwarzschild solution in Kruskal-Szekeres form) and the linear and exponential mass functions originally discovered by Waugh and Lake. We present here a semi-analytical approach that can be used to discuss some qualitative and quantitative aspects of the Vaidya metric in double-null coordinates for generic mass functions. We present also a new analytical solution corresponding to $(1/v)$-mass function.