Rindler-type geometry inside a black hole

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.