Global structure and thermodynamic property of the 4-dimensional twisted Kerr solution

Abstract

Rotating stringy black hole solutions with non-vanishing dilaton $ϕ$, antisymmetric tensor $B_{μν}$, and $U(1)$ gauge field $A_μ$ are investigated. Both Boyer-Lindquist-like and Kerr-Schild-like coordinate are constructed. The latter is utilised to construct the analytically extended spacetime. The global structure of the resulting extended spacetime is almost identical to that of the Kerr. In carrying out the analytic extension, the radial coordinate should be suitably chosen so that we can avoid singularity caused by the twisting. The thermodynamic property of the stringy black hole is examined through the injection of test bodies into the black hole. It is shown that one cannot change a black hole configuration into a naked singularity by way of throwing test bodies into the black hole. The global $O(2,3)$ symmetry and the preservation of the asymptotic flatness are discussed. When we impose stationarity, axisymmetry, and asymptotic flatness, there is no other twisting than the one pointed out by A.Sen\cite{sen}. All the other elements of $O(2,3)$ either break the asymptotic flatness, or cause only coordinate transformations and gives no physical change.