On the conformally flat Rindler-like geometry

TL;DR

This paper explores a conformally-flat, Rindler-like spacetime with a horizon, analyzing its geometry, observer acceleration, and geodesic paths, revealing hyperbolic trajectories under specific conditions.

Contribution

It introduces a time-dependent conformally-flat Rindler-like geometry and analyzes its horizon, acceleration, and geodesic structure, providing new insights into such spacetimes.

Findings

The spacetime has an apparent horizon coinciding with the causal horizon.

The scalar acceleration of static observers is constant and equals g.

Radial geodesics are hyperbolic with specific integration constants.

Abstract

The time dependent conformally-flat spherical Rindler spacetime is investigated. The geometry has an apparent horizon that coincides with the causal horizon. The scalar acceleration of a static observer is constant and equals to the acceleration $g$ from the static expression of the Rindler-like metric. The timelike radial geodesics are computed and proves to be hyperbolae when a specific choice of the constants of integration is operated.