A Vaidya-type spacetime with no singularities

TL;DR

This paper introduces a regular Vaidya-type spacetime with a mass function dependent on both time and space, ensuring finite curvature invariants and stress tensor, and explores its physical properties and energy conditions.

Contribution

It proposes a new regular Vaidya-type solution with a variable mass function, analyzing its curvature, energy conditions, and geodesic behavior, which was not previously studied.

Findings

Curvature invariants and stress tensor are finite everywhere.

Energy conditions are satisfied under specific parameter constraints.

Radial pressure peaks near the horizon, affecting geodesic acceleration.

Abstract

A regular Vaidya-type line-element is proposed in this work. The mass function depends both on the temporal and the spatial coordinates. The curvature invariants and the source stress tensor $T^{a}_{~b}$ are finite in the whole space. The energy conditions for $T^{a}_{~b}$ are satisfied if $k^{2}<2vr$, where $k$ is a positive constant and $v,r$ are coordinates. It is found that the radial pressure has a maximum very close to $r = 2m~ (r>2m), v = 2m$. The energy crossing a sphere of constant radius is akin to Lundgren-Schmekel-York quasilocal energy. The Newtonian acceleration of the timelike geodesics has an extra term (compared to the result of Piesnack and Kassner) which leads to rejecting effects.