Spinning BTZ black hole versus Kerr black hole: A closer look

By applying Newman’s algorithm, the ${\mathrm{AdS}}_3$ rotating black hole solution is “derived” from the nonrotating black hole solution of Bañados, 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 kind of “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, the transformation to Kerr-Schild-type coordinates is looked for. Indeed, such a transformation is found to exist. In these Kerr-Schild-type coordinates, a truly maximal extension of its global structure by analytically continuing to an “antigravity universe” region is carried out.