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 $p = \rho/3$ 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.