Accelerated observers and the notion of singular spacetime

TL;DR

This paper investigates the completeness of accelerated observers in spherically symmetric spacetimes, proposing that all physically acceptable observers should have complete paths, which supports the regularity of certain black hole spacetimes.

Contribution

It introduces a framework for analyzing accelerated observer paths in regular spacetimes, extending the concept of geodesic completeness to accelerated trajectories.

Findings

Accelerated observer paths are complete in certain regular black hole spacetimes.

Bound and locally unbound accelerations do not lead to incomplete trajectories.

Supports the idea that all physically acceptable observers can describe regular spacetimes fully.

Abstract

Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and, therefore, observers with arbitrary motions should be able to provide a complete physical description of the world. This suggests that in a regular spacetime, all physically acceptable observers should have complete paths. In this work we explore this idea by studying the motion of accelerated observers in spherically symmetric spacetimes and illustrate it by considering two geodesically complete black hole spacetimes recently described in the literature. We show that for bound and locally unbound accelerations, the paths of accelerated test particles are complete, providing further support to the regularity of such spacetimes.