Causal structure and the geodesics in the hairy extension of the Bertotti-Robinson spacetime

TL;DR

This paper analyzes the causal structure and geodesic behavior in a hairy extension of the Bertotti-Robinson spacetime, revealing how particles and photons move within this singular black hole in Einstein-Maxwell-Scalar theory.

Contribution

It clarifies the topology, causal structure, and geodesic behavior of this novel hairy black hole solution, extending understanding of particle dynamics in such spacetimes.

Findings

Photons can either collapse or escape to the universe's edge.

Massive particles always fall into the singularity.

Most particles eventually fall into the black hole.

Abstract

A hairy extension of the Bertotti-Robinson regular spacetime has been recently introduced in the context of the Einstein-Maxwell-Scaler theory that surprisingly is a singular black hole formed in the $S_{3}$ background spatial topology [CQG39(2022)167001]. In this research, we first clarify the topology of the spacetime based on the coordinate transformations as well as the energy-momentum configuration and the causal structure of the black hole. Furthermore, we investigate the geodesics of the null and timelike particles in this spacetime. It is shown that in the radial motion on the equatorial plane, while photons may collapse to the singularity or escape to the edge of the universe, a massive particle always collapses to the singularity. The general geodesics of null and massive particles reveal that all particles except the outgoing light ray, eventually fall into the black hole.