Source with Nonzero Radial Pressure for the Vaidya Metric

TL;DR

This paper introduces a null fluid with radial pressure as a source for the Vaidya spacetime, exploring its properties, energy flow, and a modified metric that removes singularities at the origin.

Contribution

It proposes a new anisotropic null fluid source with specific equation of state for Vaidya spacetime and investigates a singularity-free modified metric and quasilocal energy.

Findings

Radial pressure null fluid can generate Vaidya spacetime.

A modified Vaidya metric removes the origin singularity.

The energy flow aligns with Brown-York quasilocal energy.

Abstract

A null fluid with radial pressure is proposed as the source generating Vaidya spacetime. The fluid is anisotropic with no transversal pressures and $p = \rho/3$ as its equation of state, where $p$ is the isotropic pressure and $\rho$ is the energy density. The radial energy flux is inward directed when $\dot{m} > 0$ and the total energy flow crossing a surface of constant $r$ resembles the Brown-York quasilocal energy. A modified Vaidya metric removes the singularity at the origin and the corresponding QLE is investigated in terms of both $r$ and the mass $m(v)$ of the object.