Rindler-type geometry inside a black hole

TL;DR

This paper explores a Rindler-type geometry within a black hole's interior, proposing an anisotropic fluid model with unique gravitational properties and analyzing the entropy characteristics of inner spheres.

Contribution

It introduces a novel anisotropic fluid model inside black holes with constant gravitational field and studies the junction conditions on the stretched horizon.

Findings

Gravitational field is constant inside the black hole.

Inner sphere entropy is mass independent and maximally packed.

Geometry is curved despite being of Rindler type due to spherical symmetry.

Abstract

An anisotropic fluid with positive energy density and negative pressures is proposed in the black hole interior. The gravitational field is constant everywhere inside and is given by the horizon surface gravity. Even though the geometry is of Rindler type it is curved because of the spherical symmetry used and is singular at the origin. The Israel junction conditions are studied on the stretched horizon instead of using a matching process on the null surface $r = 2M$. The entropy of any inner sphere is mass independent, maximally packed and unaffected by the outer layers.