On geodesics in spherical Rindler space

TL;DR

This paper investigates the properties of geodesics in spherical Rindler spaces, analyzing their behavior and related kinematical quantities, and compares different metric formulations to understand horizon surface gravity effects.

Contribution

It provides a detailed analysis of radial geodesics in spherical Rindler spaces for two different metric forms, highlighting the role of acceleration as surface gravity.

Findings

Radial geodesics are explicitly computed for both metric forms.

The surface gravity at the horizon is identified as the constant acceleration.

Kinematical quantities of the spacetime are characterized.

Abstract

The geodesics in various spherical Rindler frames are investigated. A display of some kinematical quantities of the spacetime is given. The constant acceleration from the metric acts as the surface gravity of the horizon $r = 0$. The radial geodesics are computed both for the Balasubramanian et al. form of the spherical Rindler space and for the non-diagonal metric of Huang and Sun.