A Vaidya-type spacetime with no singularities

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 $T_b^a$ are finite in the whole space. The energy conditions for $T_b^a$ 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.

arXiv comment13 pages, no figures, version accepted for publication in Int. J. Mod. Phys. D, https://doi.org/10.1142/S0218271822501243

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