Constructing Maximal Extensions of the Vaidya Metric in Israel Coordinates: I. Integration of the Field Equations

TL;DR

This paper derives a complete representation of the Vaidya metric by directly integrating Einstein's equations, enhancing modeling capabilities in classical and semi-classical General Relativity and Astrophysics.

Contribution

It introduces a novel method for obtaining a complete Vaidya metric representation through direct integration of Einstein's equations.

Findings

Complete Vaidya metric representation achieved

Methodology for integrating Einstein's equations presented

Enhanced modeling of relativistic phenomena possible

Abstract

This paper explores a complete representation of the Vaidya model, a radial flux of radiation in the eikonal approximation, used for modeling various phenomena in both classical and semi-classical General Relativity and Astrophysics. The majority of the applications of the Vaidya model have been formulated in an incomplete representation. A complete representation is obtained here by direct integration of the Einstein field equations. We present the methodology to obtain this complete representation, and its utility in the modeling of general relativistic phenomena.