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

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.

Presentation simplified. To appear in CQG

References in corpus (4)

• Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions
• Birkhoff's Theorem for Three-Dimensional AdS Gravity
• Extremal limit of the regular charged black holes in nonlinear electrodynamics
• Charged black holes in quadratic gravity

Cited by in corpus (4)

• Classification of near-horizon geometries of extremal black holes
• Three dimensional stationary cyclic symmetric Einstein-Maxwell solutions; black holes
• Asymptotic structure of the Einstein-Maxwell theory on AdS${}_3$
• Electrically charged black hole on AdS${}_3$: scale invariance and the Smarr formula