Shuang-Qing Wu

In a previous paper [S. Q. Wu, Phys. Rev. D 83, 121502(R) (2011)], a new kind of metric ansatz was found to fairly describe all already-known black hole solutions in the ungauged Kaluza-Klein (KK) supergravity theories. That metric ansatz somewhat resembles the famous Kerr-Schild (KS) form, but it is different from the KS one in two distinct aspects. That is, apart from a global conformal factor, the metric ansatz can be written as a vacuum background spacetime plus a “perturbation” modification term, the latter of which is associated with a timelike geodesic vector field rather than a null geodesic congruence in the usual KS ansatz. Replacing the flat vacuum background metric by the (anti–)de Sitter [(A)dS] spacetime, the general rotating charged KK-(A)dS black hole solutions in all higher dimensions have been successfully constructed and put into a unified form. In this paper, we shall study this novel metric ansatz in detail, aiming at achieving some inspiration as to the construction of rotating charged AdS black holes with multiple charges in other gauged supergravity theories. We find that the traditional perturbation expansion method often successfully used in the KS form is no longer useful in our new ansatz, since here no good parameter can be chosen as a suitable perturbation indicator. In order to investigate the metric properties of the general KK-AdS solutions, in this paper we devise a new effective method, dubbed the background metric expansion method, which can be thought of as a generalization of the perturbation expansion method, to deal with the Lagrangian and all equations of motion. In addition to two previously known conditions, namely the timelike and geodesic properties of the vector, we get three additional constraints via contracting the Maxwell and Einstein equations once or twice with this timelike geodesic vector. In particular, we find that these are a simpler set of sufficient conditions to determine the vector and the dilaton scalar around the background metric, which is helpful in obtaining new exact solutions. With these five simpler equations in hand, we rederive the general rotating charged KK-(A)dS black hole solutions with spherical horizon topology and obtain new solutions with planar topology in all dimensions. It turns out that the overall calculations in finding the solution to the KK gauged supergravity can be reduced considerably, compared to the previous process, by directly solving all the field equations. It is then shown that the rotating charged KK-AdS black hole solutions can be further generalized by introducing one or two arbitrary constants, while the black hole solutions with the planar AdS background metric in all higher dimensions are newly obtained.

I construct exact solutions for general nonextremal rotating, charged Kaluza-Klein black holes with a cosmological constant and with arbitrary angular momenta in all higher dimensions. I then investigate their thermodynamics and find their generalizations with the Newman-Unti-Tamburino charges. The metrics are given in both Boyer-Lindquist coordinates and a form very similar to the famous Kerr-Schild ansatz, which highlights its potential application to include multiple electric charges into solutions yet to be found in gauged supergravity. It is also observed that the metric ansatz in D=4 dimensions is similar to those previously suggested by Yilmaz and later by Bekenstein.

We study the thermodynamics of G\"odel-type rotating charged black holes in five-dimensional minimal supergravity. These black holes exhibit some peculiar features such as the presence of closed timelike curves and the absence of a globally spatial-like Cauchy surface. We explicitly compute their energies, angular momenta, and electric charges that are consistent with the first law of thermodynamics. Besides, we extend the covariant anomaly cancellation method, as well as the approach of the effective action, to derive their Hawking fluxes. Both the methods of the anomaly cancellation and the effective action give the same Hawking fluxes as those from the Planck distribution for blackbody radiation in the background of the charged rotating G\"odel black holes. Our results further support that Hawking radiation is a quantum phenomenon arising at the event horizon.

We study the thermodynamics of G\"{o}del-type rotating charged black holes in five-dimensional minimal supergravity. These black holes exhibit some peculiar features such as the presence of closed time-like curves and the absence of globally spatial-like Cauchy surface. We explicitly compute their energies, angular momenta, and electric charges that are consistent with the first law of thermodynamics. Besides, We extend the covariant anomaly cancellation method, as well as the approach of the effective action, to derive their Hawking fluxes. Both the methods of the anomaly cancellation and effective action give the same Hawking fluxes as those from Planck distribution for blackbody radiation in the background of the charged rotating G\"{o}del black holes. Our results further support that Hawking radiation is a quantum phenomenon arising at the event horizon.

It is shown that the Dirac equation is separable by variables in a five-dimensional rotating Kerr-(anti-)de Sitter black hole with two independent angular momenta. A first order symmetry operator that commutes with the Dirac operator is constructed in terms of a rank-three Killing-Yano tensor whose square is a second order symmetric Stackel-Killing tensor admitted by the five-dimensional Kerr-(anti-)de Sitter spacetime. We highlight the construction procedure of such a symmetry operator. In addition, the first law of black hole thermodynamics has been extended to the case that the cosmological constant can be viewed as a thermodynamical variable.