Anisotropic fluid inside a relativistic star

TL;DR

This paper proposes an anisotropic fluid model within relativistic stars that exhibits constant gravitational acceleration consistent with MOND, with unique energy density and pressure profiles affecting the star's internal and external spacetime.

Contribution

It introduces a novel anisotropic fluid model with variable energy density and negative pressure, aligning with MOND-like gravitational behavior inside and outside stars.

Findings

Gravitational field is constant outside stars, matching MOND predictions.

Inside stars, acceleration depends on mass and radius, remaining constant but variable.

Active gravitational energy on the horizon is negative, similar to Rindler space.

Abstract

An anisotropic fluid with variable energy density and negative pressure is proposed, both outside and inside stars. The gravitational field is constant everywhere in free space (if we neglect the local contributions) and its value is of the order of $g = 10^{-8} cm/s^{2}$, in accordance with MOND model. With $\rho,~ p \propto 1/r$, the acceleration is also constant inside stars but the value is different from one star to another and depends on their mass $M$ and radius $R$. In spite of the fact that the spacetime is of Rindler type and curved even far from a local mass, the active gravitational energy on the horizon is $-1/4g$, as for the flat Rindler space, excepting the negative sign.