On a free of centrifugal acceleration spacetime

Abstract

A static spacetime with no centrifugal repulsion, previously studied by Dadhich, is investigate in this paper. The source of curvature is considered to be an anisotropic fluid with $\rho = -p_{r}$ and constant angular pressures. The positive parameter from the line-element is interpreted as the invariant acceleration of a static observer. The timelike and null geodesics of the spacetime are examined. A regularized form of the metric is proposed, rendering it finite at the origin. The energy density of the fluid becomes finite and negative for any $r$ and all the pressures are positive throughout the spacetime. The Tolman-Komar energy $W(r)$ is computed and proves to be smaller than that one calculated with the Dadhich metric.