Tomimatsu-Sato geometries, holography and quantum gravity

We analyze the $\delta=2$ Tomimatsu-Sato spacetime in the context of the proposed Kerr/CFT correspondence. This 4-dimensional vacuum spacetime is asymptotically flat and has a well-defined ADM mass and angular momentum, but also involves several exotic features including a naked ring singularity, and two disjoint Killing horizons separated by a region with closed timelike curves and a rod-like conical singularity. We demonstrate that the near horizon geometry belongs to a general class of Ricci-flat metrics with $SL(2,\mathbb{R})\times U(1)$ symmetry that includes both the extremal Kerr and extremal Kerr-bolt geometries. We calculate the central charge and temperature for the CFT dual to this spacetime and confirm the Cardy formula reproduces the Bekenstein-Hawking entropy. We find that all of the basic parameters of the dual CFT are most naturally expressed in terms of charges defined intrinsically on the horizon, which are distinct from the ADM charges in this geometry.Comment: 20+1 pages, 3 figures, changed title, expanded discussion, matches version published in CQ

An action for the exact string black hole

A local action is constructed describing the exact string black hole discovered by Dijkgraaf, Verlinde and Verlinde in 1992. It turns out to be a special 2D Maxwell-dilaton gravity theory, linear in curvature and field strength. Two constants of motion exist: mass M>1, determined by the level k, and U(1)-charge Q>0, determined by the value of the dilaton at the origin. ADM mass, Hawking temperature T_H \propto \sqrt{1-1/M} and Bekenstein-Hawking entropy are derived and studied in detail. Winding/momentum mode duality implies the existence of a similar action, arising from a branch ambiguity, which describes the exact string naked singularity. In the strong coupling limit the solution dual to AdS_2 is found to be the 5D Schwarzschild black hole. Some applications to black hole thermodynamics and 2D string theory are discussed and generalizations - supersymmetric extension, coupling to matter and critical collapse, quantization - are pointed out.Comment: 41 pages, 2 eps figures, dedicated to Wolfgang Kummer on occasion of his Emeritierung; v2: added ref; v3: extended discussion in sections 3.2, 3.3 and at the end of 5.3 by adding 2 pages of clarifying text; updated refs; corrected typo