On the near horizon approximation for the Schwarzschild black hole

TL;DR

This paper explores a model where an anisotropic fluid with negative radial pressure exists near a Schwarzschild black hole's horizon, revealing a Rindler-like acceleration and stress tensor structure similar to black hole interiors.

Contribution

It introduces a near-horizon approximation involving an anisotropic fluid with negative pressure, connecting the stress tensor structure to black hole interior models.

Findings

Radial acceleration has a Rindler form.

Stress tensor resembles black hole interior models.

Energy density depends only on black hole mass.

Abstract

An anisotropic fluid with a negative radial pressure $p = - \rho$ is supposed to exist near the horizon of a Schwarzschild black hole. The constant energy density $\rho$ depends only on the black hole mass. The radial acceleration of the static observers is constant but its modulus has exactly the Rindler form, as was recently suggested by Dahia and Felix da Silva. The structure of the stress tensor is similar with that obtained previously for the interior region of a black hole, excepting the time dependence.