Spinning BTZ Black Hole versus Kerr Black Hole : A Closer Look

TL;DR

This paper explores different coordinate representations of rotating BTZ black holes, deriving new forms via Newman’s algorithm, and analyzes their global structure and extensions, including the connection to Kerr black holes.

Contribution

It introduces Kerr-Schild-type coordinates for rotating BTZ black holes and performs a maximal extension of their global structure, revealing new insights into their geometry.

Findings

Derived Kerr-Schild coordinates for rotating BTZ black holes

Found a transformation connecting Boyer-Lindquist and Kerr-Schild coordinates

Performed maximal extension including antigravity universe region

Abstract

By applying Newman's algorithm, the AdS_3 rotating black hole solution is ``derived'' from the nonrotating black hole solution of Banados, Teitelboim, and Zanelli (BTZ). The rotating BTZ solution derived in this fashion is given in ``Boyer-Lindquist-type'' coordinates whereas the form of the solution originally given by BTZ is given in a kind of an ``unfamiliar'' coordinates which are related to each other by a transformation of time coordinate alone. The relative physical meaning between these two time coordinates is carefully studied. Since the Kerr-type and Boyer-Lindquist-type coordinates for rotating BTZ solution are newly found via Newman's algorithm, next, the transformation to Kerr-Schild-type coordinates is looked for. Indeed, such transformation is found to exist. And in this Kerr-Schild-type coordinates, truely maximal extension of its global structure by analytically continuing to ``antigravity universe'' region is carried out.