Boundary stress tensors for spherically symmetric conformal Rindler observers

TL;DR

This paper analyzes boundary energy-momentum tensors for static observers in conformally flat Rindler spacetime, revealing positive surface energy, negative transverse pressures, and a connection between surface degrees of freedom and black hole entropy.

Contribution

It provides a detailed computation of boundary stress tensors, kinematical parameters, and entropy relations for static observers in conformal Rindler geometry, linking them to black hole thermodynamics.

Findings

Surface energy is positive away from the Planck scale.

Transversal pressures are negative.

Surface entropy matches black hole horizon entropy.

Abstract

The boundary energy - momentum tensors for a static observer in the conformally flat Rindler geometry are considered. We found the surface energy is positive far form the Planck world but the transversal pressures are negative. The kinematical parameters associated to a nongeodesic congruence of static observers are computed. The entropy $S$ corresponding to the degrees of freedom on the two surface of constant $\rho$ and $t$ equals the horizon entropy of a black hole with a time dependent mass and the Padmanabhan expression $E = 2 S T$ is obeyed. The two surface shear tensor is vanishing but the coefficient of the bulk viscosity $\zeta$ is $1/16 \pi$ and therefore the negative pressure due to it acts as a surface tension.