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

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 quasi-local 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.