Non-Extremal Rotating Black Holes in Five-Dimensional Gauged Supergravity

Supersymmetric black holes in five-dimensional gauged supergravity must necessarily be rotating, and so in order to study the passage to black holes away from supersymmetry, it is of great interest to obtain non-extremal black holes that again have non-zero rotation. In this paper we find a simple framework for describing non-extremal rotating black holes in five-dimensional gauged supergravities. Using this framework, we are able to construct a new solution, describing the general single-charge solution of N=2 gauged supergravity, with arbitrary values for the two rotation parameters. Previously-obtained solutions with two or three equal charges also assume a much simpler form in the new framework, as also does the general solution with three unequal charges in ungauged N=2 supergravity. We discuss the thermodynamics and BPS limit of the new single-charge solutions, and we discuss the separability of the Hamilton-Jacobi and Klein-Gordan equations in these backgrounds.Comment: Latex, 12 pages. Mis-statement about separability of Hamilton-Jacobi and Klein-Gordon equations correcte

License protection with a tamper-resistant token

Content protection mechanisms are intended to enforce the usage rights on the content. These usage rights are carried by a license. Sometimes, a license even carries the key that is used to unlock the protected content. Unfortunately, license protection is difficult, yet it is important for digital rights management (DRM). Not many license protection schemes are available, and most if not all are proprietary. In this paper, we present a license protection scheme, which exploits tamper-resistant cryptographic hardware. The confidentiality and integrity of the license or parts thereof can be assured with our protection scheme. In addition, the keys to unlock the protected content are always protected and stored securely as part of the license. We verify secrecy and authentication aspects of one of our protocols. We implement the scheme in a prototype to assess the performance.\ud This project is funded by Telematica Instituut, The Netherlands

Secure Audit Logging with Tamper-Resistant Hardware

Secure perimeter schemes (e.g. DRM) and tracing traitor schemes (e.g. watermarking, audit logging) strive to mitigate the problems of content escaping the control of the rights holder. Secure audit logging records the user's actions on content and enables detection of some forms of tampering with the logs. We implement Schneier and Kelsey's secure audit logging protocol, strengthening the protocol by using tamper-resistant hardware (an iButton) in two ways: Firstly our implementation of the protocol works offline as well as online. Secondly, we use unforgeable time stamps to increase the possibilities of fraud detection. We provide a performance assessment of our implementation to show under which circumstances the protocol is practical to use

Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions

A generalisation of the four-dimensional Kerr-de Sitter metrics to include a NUT charge is well known, and is included within a class of metrics obtained by Plebanski. In this paper, we study a related class of Kerr-Taub-NUT-de Sitter metrics in arbitrary dimensions D \ge 6, which contain three non-trivial continuous parameters, namely the mass, the NUT charge, and a (single) angular momentum. We demonstrate the separability of the Hamilton-Jacobi and wave equations, we construct a closely-related rank-2 Staeckel-Killing tensor, and we show how the metrics can be written in a double Kerr-Schild form. Our results encompass the case of the Kerr-de Sitter metrics in arbitrary dimension, with all but one rotation parameter vanishing. Finally, we consider the real Euclidean-signature continuations of the metrics, and show how in a limit they give rise to certain recently-obtained complete non-singular compact Einstein manifolds.Comment: Author added, title changed, references added, focus of paper changed to Killing tensors and separability. Latex, 13 page

Non-extremal Charged Rotating Black Holes in Seven-Dimensional Gauged Supergravity

We obtain the solution for non-extremal charged rotating black holes in seven-dimensional gauged supergravity, in the case where the three rotation parameters are set equal. There are two independent charges, corresponding to gauge fields in the U(1)xU(1) abelian subgroup of the SO(5) gauge group. A new feature in these solutions, not seen previously in lower-dimensional examples, is that the first-order "odd-dimensional self-duality" equation for the 4-form field strength plays a non-trivial role. We also study the BPS limit of our solutions where the black holes become supersymmetric. Our results are of significance for the AdS_7/CFT_6 correspondence in M-theory.Comment: Latex, 12 pages, typos corrected and a reference adde

BPS Geometries and AdS Bubbles

Recently, 1/2-BPS AdS bubble solutions have been obtained by Lin, Lunin and Maldacena, which correspond to Fermi droplets in phase space in the dual CFT picture. They can be thought of as generalisations of 1/2-BPS AdS black hole solutions in five or seven dimensional gauged supergravity. In this paper, we extend these solutions by invoking additional gauge fields and scalar fields in the supergravity Lagrangians, thereby obtaining AdS bubble generalisations of the previously-known multi-charge AdS black solutions of gauged supergravity. We also obtain analogous AdS bubble solutions in four-dimensional gauged supergravity. Our solutions generically preserve supersymmetry fractions 1/4, 1/8 and 1/8 in seven, five and four dimensions respectively. They can be lifted to M-theory or type IIB string theory, using previously known formulae for the consistent Pauli sphere reductions that yield the gauged supergravities. We also find similar solutions in six-dimensional gauged supergravity, and discuss their lift to the massive type IIA theory.Comment: Latex, 11 page

Pseudo-supersymmetry, Consistent Sphere Reduction and Killing Spinors for the Bosonic String

Certain supergravity theories admit a remarkable consistent dimensional reduction in which the internal space is a sphere. Examples include type IIB supergravity reduced on S^5, and eleven-dimensional supergravity reduced on S^4 or S^7. Consistency means that any solution of the dimensionally-reduced theory lifts to give a solution in the higher dimension. Although supersymmetry seems to play a role in the consistency of these reductions, it cannot be the whole story since consistent sphere reductions of non-supersymmetric theories are also known, such as the reduction of the effective action of the bosonic string in any dimension D on either a 3-sphere or a (D-3)-sphere, retaining the gauge bosons of SO(4) or SO(D-2) respectively. We show that although there is no supersymmetry, there is nevertheless a natural Killing spinor equation for the D-dimensional bosonic string. A projection of the full integrability condition for these Killing spinors gives rise to the bosonic equations of motion (just as happens in the supergravity examples). Thus it appears that by extending the notion of supersymmetry to "pseudo-supersymmetry" in this way, one may be able to obtain a broader understanding of a relation between Killing spinors and consistent sphere reductions.Comment: Latex, 15 page

Kerr-de Sitter Black Holes with NUT Charges

The four-dimensional Kerr-de Sitter and Kerr-AdS black hole metrics have cohomogeneity 2, and they admit a generalisation in which an additional parameter characterising a NUT charge is included. In this paper, we study the higher-dimensional Kerr-AdS metrics, specialised to cohomogeneity 2 by appropriate restrictions on their rotation parameters, and we show how they too admit a generalisation in which an additional NUT-type parameter is introduced. We discuss also the supersymmetric limits of the new metrics. If one performs a Wick rotation to Euclidean spacetime signature, these yield new Einstein-Sasaki metrics in odd dimensions, and Ricci-flat metrics in even dimensions. We also study the five-dimensional Kerr-AdS black holes in detail. Although in this particular case the NUT parameter is trivial, our investigation reveals the remarkable feature that a five-dimensional Kerr-AdS ``over-rotating'' metric is equivalent, after performing a coordinate transformation, to an under-rotating Kerr-AdS metric.Comment: Latex, 21 page

General Supersymmetric Solutions of Five-Dimensional Supergravity

The classification of 1/4-supersymmetric solutions of five dimensional gauged supergravity coupled to arbitrary many abelian vector multiplets, which was initiated in hep-th/0401129, is completed. The structure of all solutions for which the Killing vector constructed from the Killing spinor is null is investigated in both the gauged and the ungauged theories and some new solutions are constructed.Comment: 24 pages, references added, uses JHEP3.cl

Charged Rotating Black Holes in Four-Dimensional Gauged and Ungauged Supergravities

We study four-dimensional non-extremal charged rotating black holes in ungauged and gauged supergravity. In the ungauged case, we obtain rotating black holes with four independent charges, as solutions of N=2 supergravity coupled to three abelian vector multiplets. This is done by reducing the theory along the time direction to three dimensions, where it has an O(4,4) global symmetry. Applied to the reduction of the uncharged Kerr metric, O(1,1)^4\subset O(4,4) transformations generate new solutions that correspond, after lifting back to four dimensions, to the introduction of four independent electromagnetic charges. In the case where these charges are set pairwise equal, we then generalise the four-dimensional rotating black holes to solutions of gauged N=4 supergravity, with mass, angular momentum and two independent electromagnetic charges. The dilaton and axion fields are non-constant. We also find generalisations of the gauged and ungauged solutions to include the NUT parameter, and for the ungauged solutions, the acceleration parameter too. The solutions in gauged supergravity provide new gravitational backgrounds for a further study of the AdS_4/CFT_3 correspondence at non-zero temperature.Comment: Latex, 30 page