Kinematic quantities for a spherical distribution of uniformly accelerated observers

TL;DR

This paper analyzes the kinematic properties of a spherical distribution of uniformly accelerated observers, revealing divergence at the event horizon and linking surface gravity to proper acceleration.

Contribution

It provides a detailed study of shear, expansion, and surface gravity for a nongeodesic congruence in spherical Rindler coordinates, highlighting new insights into horizon behavior.

Findings

Shear tensor components diverge at the event horizon.

Surface gravity equals the proper acceleration of observers.

Raychaudhuri equation holds for the congruence.

Abstract

The kinematical quantities derived from the velocity field of a nongeodesic congruence are studied. We found the shear tensor components are finite in time but diverge at the event horizon of the spacetime located at $\rho = 0$. The surface gravity on the horizon is just the proper acceleration of the uniformly expanding distribution of observers, in spherical Rindler coordinates. The Raychaudhuri equation is fulfilled for the congruence of particles worldlines.