On a star with static conformally flat geometry inside

TL;DR

This paper investigates a static, conformally flat star with constant positive energy density and negative pressure, revealing a repulsive gravitational field and finite curvature invariants, challenging typical energy condition expectations.

Contribution

It introduces a model of a star with negative pressure inside, analyzing its geometric and physical properties within a conformally flat spacetime framework.

Findings

Gravitational field inside is repulsive due to negative pressure.

Ricci and Kretschmann invariants are finite inside the star.

Energy conditions are mostly satisfied except the strong energy condition.

Abstract

The properties of a star with constant positive energy density inside (as for the Schwarzschild interior geometry) and a negative pressure are investigated, using a static conformally flat spacetime. Because of the negative pressure, the gravitational field inside is repulsive. Ricci and Kretschmann curvature invariants are finite. The energy conditions for the stress tensor of the perfect fluid are satisfied, excepting the strong energy condition which is not obeyed for $r<R/\sqrt{2}$, where $R$ is the radius of the object. The Komar mass is calculated and discussed.