Source with Nonzero Radial Pressure for the Vaidya Metric

A null fluid with radial pressure is proposed as the source generating Vaidya spacetime. The fluid is anisotropic with no transversal pressures and $p = \rho/3$asitsequationofstate,where$p$istheisotropicpressureand$\rho$istheenergydensity\mathrm{.}Theradialenergyfluxisinwarddirectedwhen$\dot{m} > 0$andthetotalenergyflowcrossingasurfaceofconstant$r$ 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.