Killing-Yano tensor and supersymmetry of the self-dual Plebanski-Demianski solution

We explore various aspects of the self-dual Pleba\'nski-Demia\'nski family in the Euclidean Einstein-Maxwell-$\Lambda$ system. The Killing-Yano tensor which was recently found by Yasui and one of the present authors allows us to prove that the self-dual Pleba\'nski-Demia\'nski metric can be brought into the self-dual Carter metric by an orientation-reversing coordinate transformation. We show that the self-dual Pleba\'nski-Demia\'nski solution admits two independent Killing spinors in the framework of $N=2$ minimal gauged supergravity, whereas the non-self-dual solution admits only a single Killing spinor. This can be demonstrated by casting the self-dual Pleba\'nski-Demia\'nski metric into two distinct Przanowski-Tod forms. As a by-product, a new example of the three-dimensional Einstein-Weyl space is presented. We also prove that the self-dual Pleba\'nski-Demia\'nski metric falls into two different Calderbank-Pedersen families, which are determined by a single function subjected to a linear equation on the two dimensional hyperbolic space. Furthermore, we consider the hyper-K\"ahler case for which the metric falls into the Gibbons-Hawking class. We find that the condition for the nonexistence of Dirac-Misner string enforces the solution with a nonvanishing acceleration parameter to the Eguchi-Hanson space.Comment: 41 pages, v3: minor modifications, refs added, published version in CQ

Black Hole in the Expanding Universe with Arbitrary Power-Law Expansion

We present a time-dependent and spatially inhomogeneous solution that interpolates the extremal Reissner-Nordstr\"om (RN) black hole and the Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe with arbitrary power-law expansion. It is an exact solution of the $D$-dimensional Einstein-"Maxwell"-dilaton system, where two Abelian gauge fields couple to the dilaton with different coupling constants, and the dilaton field has a Liouville-type exponential potential. It is shown that the system satisfies the weak energy condition. The solution involves two harmonic functions on a $(D-1)$-dimensional Ricci-flat base space. In the case where the harmonics have a single-point source on the Euclidean space, we find that the spacetime describes a spherically symmetric charged black hole in the FLRW universe, which is characterized by three parameters: the steepness parameter of the dilaton potential $n_T$, the U$(1)$ charge $Q$, and the "nonextremality" $\tau$. In contrast with the extremal RN solution, the spacetime admits a nondegenerate Killing horizon unless these parameters are finely tuned. The global spacetime structures are discussed in detail.Comment: 22 pages, 8 figures, 1 table; v2: typos corrected, references added, version to appear in PR

Geometry of Killing spinors in neutral signature

We classify the supersymmetric solutions of minimal $N=2$ gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and whether the vector field constructed as a bilinear of the Killing spinor is null or non-null. In neutral signature the bilinear vector field can be spacelike, which is a new feature not arising in Lorentzian signature. In the $\Lambda<0$ non-null case, the canonical form of the metric is described by a fibration over a three-dimensional base space that has $\text{U}(1)$ holonomy with torsion. We find that a generalized monopole equation determines the twist of the bilinear Killing field, which is reminiscent of an Einstein-Weyl structure. If, moreover, the electromagnetic field strength is self-dual, one gets the Kleinian signature analogue of the Przanowski-Tod class of metrics, namely a pseudo-hermitian spacetime determined by solutions of the continuous Toda equation, conformal to a scalar-flat pseudo-K\"ahler manifold, and admitting in addition a charged conformal Killing spinor. In the $\Lambda<0$ null case, the supersymmetric solutions define an integrable null K\"ahler structure. In the $\Lambda>0$ non-null case, the manifold is a fibration over a Lorentzian Gauduchon-Tod base space. Finally, in the $\Lambda>0$ null class, the metric is contained in the Kundt family, and it turns out that the holonomy is reduced to ${\rm Sim}(1)\times{\rm Sim}(1)$. There appear no self-dual solutions in the null class for either sign of the cosmological constant.Comment: 40 pages, uses JHEP3.cls. v2: Appendix and ref. added. v3: Published versio

Black hole solutions in string theory

Supersymmetric solutions of supergravity have been of particular importance in the advances of string theory. This article reviews the current status of black hole solutions in higher-dimensional supergravity theories. We discuss primarily the gravitational aspects of supersymmetric black holes and their relatives in various dimensions. Supersymmetric solutions and their systematic derivation are reviewed with prime examples. We also study the stationary or dynamically intersecting branes in ten and eleven-dimensions, which provide a number of interesting black objects via the dimensional reduction and duality transformations.Comment: Invited review for Prog. Theor. Phys. Suppl, 41 pages, 2 figures, 2 tables; v2: typos corrected, references adde