On maximal analytical extension of the Vaidya metric

TL;DR

This paper derives the maximal analytical extension of the Vaidya metric with a linear mass function, providing explicit metric expressions and Carter-Penrose diagrams, and suggests broader applicability to more general mass behaviors.

Contribution

It introduces a new diagonal coordinate system for the Vaidya metric and explicitly constructs its maximal extension and Penrose diagrams.

Findings

Explicit analytical expressions for metric functions in diagonal coordinates.

Construction of Carter-Penrose diagrams for various cases.

Global geometry potentially extends to more general mass functions.

Abstract

The classical Vaidya metric is transformed to the special diagonal coordinates in the case of the linear mass function allowing rather easy treatment. We find the exact analytical expressions for metric functions in these diagonal coordinates. Using these coordinates, we elaborate the maximum analytic extension of the Vaidya metric with a linear growth of the black hole mass and construct the corresponding Carter-Penrose diagrams for different specific cases. The derived global geometry seemingly is valid also for a more general behavior of the black hole mass in the Vaidya metric.