Extremal limit for charged and rotating 2+1-dimensional black holes and Bertotti-Robinson geometry

TL;DR

This paper investigates 2+1-dimensional analogues of Bertotti-Robinson spacetimes, revealing that such solutions are either static uncharged or rotating uncharged, and explores their energy and angular momentum properties.

Contribution

It demonstrates that BR-like solutions in 2+1 dimensions are either static or uncharged rotating, clarifying the incompatibility between charge and rotation in these spacetimes.

Findings

BR-like solutions are either static or uncharged rotating.

Inconsistency exists between charge and rotation in these solutions.

Quasilocal energy and angular momentum are constant and boundary-independent.

Abstract

We consider 2+1--dimensional analogues of the Bertotti-Robinson (BR) spacetimes in the sense that the coefficient at the angular part is a constant. We show that such BR-like solutions are either pure static or uncharged rotating. We trace the origin of the inconsistency between a charge and rotation, considering the BR-like spacetime as a result of the limiting transition of a non-extremal black hole to the extremal state. We also find that the quasilocal energy and angular momentum of such BR-like spacetimes calculated within the boundary $l=const$ ($l$ is the proper distance) are constants independent of the position of the boundary.