Topological classes of thermodynamics of rotating AdS black holes

Abstract

In this paper, we investigate the topological numbers for the singly-rotating Kerr-AdS black holes in all dimensions and the four-dimensional Kerr-Newman-AdS black hole. We show that for uncharged AdS black holes, the rotation parameter has a significant impact on the topological number, and for rotating AdS black holes, the dimension of spacetimes has an important effect on the topological number. In addition, it indicates that the electric charge parameter has no impact on the topological number of rotating AdS black holes because of the four-dimensional Kerr-AdS and Kerr-Newman-AdS black holes have the same topological numbers. Furthermore, we propose a conjecture that, given an AdS black hole, the difference between its topological number and that of its corresponding non-AdS black hole is always unity.

Classifying topology of consistent thermodynamics of four-dimensional Lorentzian NUT-charged spacetimes

“…Note that the topological number W still stays the same if the pressure takes another arbitrary value. Additionally, similar to the results given above for the RN-NUT spacetime and KN-NUT spacetime, it also gives a counterexample that significantly differs from the conclusions reached in all prior works [52][53][54][55][56][57][58][59][60][61], which state that a black hole solution only has one certain topological number, independent of the values of the solution parameters.…”

“…Thus, the whole class of four-dimensional NUTcharged spacetimes should be viewed as generic black holes from the viewpoint of the thermodynamic topological approach. Furthermore, the RN-NUT spacetime, KN-NUT spacetime, and RN-NUT-AdS spacetime provide three counterexamples that significantly differs from the conclusions reached in all prior works [52][53][54][55][56][57][58][59][60][61], which conclude that a black hole solution only has one definite topological number, independent of the values of the solution parameters.…”

“…Based on the local property of the zero points, for the RN-NUT spacetime, we have the topological number W = −1 when the parameter values n > q, and W = 1 − 1 = 0 when n ≤ q. Thus, it provides the first example violates the consensus in all previous works [52][53][54][55][56][57][58][59][60][61] that one black hole solution has only one definite topological number, regardless of the values of the solution parameters. In addition, since the topological number of the Taub-NUT spacetime is −1, while that of RN-NUT spacetimes is −1 or 0, it implies that the electric charge parameter has an important effect on the topological number for the neutral static Taub-NUT spacetime.…”

“…Because of its simplicity and easy maneuverability of the procedure, the thermodynamic topological approach proposed in Ref. [52] soon attracted a great deal of attention and was then successfully applied to investigate the topological numbers of some known black hole solutions [53][54][55][56][57][58][59][60][61]. It is natural to study the topological numbers of NUT-charged spacetimes to determine whether they are black holes.…”

On Thermal Stability of Hairy Black Holes

“…in certain spacetime foam situations, microscopic black holes play a crucial rôle [46,47]). Verification of the conjecture of [45] has also been given for the case of rotating black holes of both Kerr (in d+1 spacetime dimensions) and Kerr-Newman (in (3+1) spacetime dimensions) type in [48], including AdS rotating black holes [49], and also higher-curvature black holes of Lovelock [50] or higher-dimensional GB AdS type [51].…”