N-dimensional Vaidya metric with cosmological constant in double-null coordinates

TL;DR

This paper extends a method for constructing Vaidya metrics in double-null coordinates to higher dimensions and includes a cosmological constant, providing new solutions and insights into causal structures relevant for gravitational collapse.

Contribution

It introduces a generalized approach for n-dimensional Vaidya metrics with cosmological constant, including new exact solutions and a qualitative analysis of null-geodesics.

Findings

Extended Vaidya metric construction to n-dimensions

Presented new exact solutions with cosmological constant

Analyzed causal structure via null-geodesics

Abstract

A recently proposed approach to the construction of the Vaidya metric in double-null coordinates for generic mass functions is extended to the $n$-dimensional $(n>2)$ case and to allow the inclusion of a cosmological constant. The approach is based on a qualitative study of the null-geodesics, allowing the description of light-cones and revealing many features of the underlying causal structure. Possible applications are illustrated by explicit examples. Some new exact solutions are also presented and discussed. The results presented here can simplify considerably the study of spherically symmetric gravitational collapse and mass accretion in arbitrary dimensions.