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Register a new userThermodynamics of five-dimensional static three-charge STU black holes with squashed horizons
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We present a new expression for the five-dimensional static Kaluza-Klein black hole solution with squashed $S^3$ horizons and three different charge parameters. This black hole solution belongs to $D = 5$ $N = 2$ supergravity theory, its spacetime is locally asymptotically flat and has a spatial infinity $R times S^1 hookrightarrow S^2$. The form of the solution is extraordinary simple and permits us very conveniently to calculate its conserved charges by using the counterterm method. It is further shown that our thermodynamical quantities perfectly obey both the differential and the integral first laws of black hole thermodynamics if the length of the compact extra-dimension can be viewed as a thermodynamical variable.
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We study gravitational and electromagnetic perturbation around the squashed Kaluza-Klein black holes with charge. Since the black hole spacetime focused on this paper have $SU(2) times U(1) simeq U(2)$ symmetry, we can separate the variables of the equations for perturbations by using Wigner function $D^{J}_{KM}$ which is the irreducible representation of the symmetry. In this paper, we mainly treat $J=0$ modes which preserve $SU(2)$ symmetry. We derive the master equations for the $J=0$ modes and discuss the stability of these modes. We show that the modes of $J = 0$ and $ K=0,pm 2$ and the modes of $K = pm (J + 2)$ are stable against small perturbations from the positivity of the effective potential. As for $J = 0, K=pm 1$ modes, since there are domains where the effective potential is negative except for maximally charged case, it is hard to show the stability of these modes in general. To show stability for $J = 0, K=pm 1$ modes in general is open issue. However, we can show the stability for $J = 0, K=pm 1$ modes in maximally charged case where the effective potential are positive out side of the horizon.
We use the recipe of arXiv:1003.2974 to find half-BPS near-horizon geometries in the t$^3$ model of $N=2$, $D=4$ gauged supergravity, and explicitely construct some new examples. Among these are black holes with noncompact horizons, but also with spherical horizons that have conical singularities (spikes) at one of the two poles. A particular family of them is extended to the full black hole geometry. Applying a double-Wick rotation to the near-horizon region, we obtain solutions with NUT charge that asymptote to curved domain walls with AdS$_3$ world volume. These new solutions may provide interesting testgrounds to address fundamental questions related to quantum gravity and holography.
The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)times U(1)simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.
We derive new identities for the thermodynamic variables of five-dimensional, asymptotically flat, stationary and biaxisymmetric vacuum black holes. These identities depend on the topology of the solution and include contributions arising from certain topological charges. The proof employs the harmonic map formulation of the vacuum Einstein equations for solutions with these symmetries.
We examine an exact solution which represents a charged black hole in a Kaluza-Klein universe in the five-dimensional Einstein-Maxwell theory. The spacetime approaches to the five-dimensional Kasner solution that describes expanding three dimensions and shrinking an extra dimension in the far region. The metric is continuous but not smooth at the black hole horizon. There appears a mild curvature singularity that a free-fall observer can traverse the horizon. The horizon is a squashed three-sphere with a constant size, and the metric is approximately static near the horizon.
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