Comment on "The entropy of a hole in spacetime"

TL;DR

This paper critically examines the concept of horizons in spherical Rindler space, arguing that the previously identified horizon is an artifact of a static approximation and not a true physical horizon.

Contribution

It challenges prior claims by showing the absence of a genuine horizon in spherical Rindler space, emphasizing the importance of correct geometric and dynamic considerations.

Findings

No actual horizon of size R0 exists in spherical Rindler space.

The apparent horizon arises only from a static approximation, not the true geometry.

The near-horizon geometry cancels the time dependence, invalidating previous assumptions.

Abstract

Balasubramanian, Czech, Chowdhury and de Boer \cite{BCCdB} studied a "spherical Rindler space" and found that accelerating observers are causally disconnected from a spherical region located at the origin of Minkowski space. We show that there is no any horizon of size $R_{0}$ (which is related to the chosen initial conditions) and the event horizon at $r = 0$ is obtained only from the two-dimensional ($r, t$) static restriction. Their near-horizon geometry cancels the time dependence of the original metric and therefore the approximation used is doubtful.