On a free of centrifugal acceleration spacetime

TL;DR

This paper investigates a static spacetime with no centrifugal acceleration, analyzing its geometric and physical properties, including geodesics, energy conditions, and a regularized metric form, revealing finite negative energy density and positive pressures.

Contribution

It introduces a regularized metric for a centrifugal-free spacetime with an anisotropic fluid source, extending previous models and analyzing its physical and geometric features.

Findings

Energy density becomes finite and negative at all radii.

All pressures are positive throughout the spacetime.

The regularized metric is finite at the origin.

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.