Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four-dimensional example with a non-zero cosmological constant was exhibited by Ghanam and Thompson. Here we reduce the problem of finding the general $n$-dimensional Einstein metric of SIM(n-2) holonomy, with and without a cosmological constant, to solving a set linear generalised Laplace and Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit examples may be constructed in terms of generalised harmonic functions. A dimensional reduction of these multi-centre solutions gives new time-dependent Kaluza-Klein black holes and monopoles, including time-dependent black holes in a cosmological background whose spatial sections have non-vanishing curvature.Comment: Typos corrected; 29 page

Phases of 4D Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics

Recent results show that when non-linear electrodynamics is considered the no-scalar-hair theorems in the scalar-tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented. What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to non-linear electrodynamics in a special class of scalar-tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other four phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar-tensor theories considered, the black holes have a single, non-degenerate horizon, i.e., their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicates that a phase transition may occur.Comment: 18 pages, 8 figures, new phases, figures, clarifying remarks and acknowledgements adde

More about Birkhoff's Invariant and Thorne's Hoop Conjecture for Horizons

A recent precise formulation of the hoop conjecture in four spacetime dimensions is that the Birkhoff invariant $\beta$ (the least maximal length of any sweepout or foliation by circles) of an apparent horizon of energy $E$ and area $A$ should satisfy $\beta \le 4 \pi E$. This conjecture together with the Cosmic Censorship or Isoperimetric inequality implies that the length $\ell$ of the shortest non-trivial closed geodesic satisfies $\ell^2 \le \pi A$. We have tested these conjectures on the horizons of all four-charged rotating black hole solutions of ungauged supergravity theories and find that they always hold. They continue to hold in the the presence of a negative cosmological constant, and for multi-charged rotating solutions in gauged supergravity. Surprisingly, they also hold for the Ernst-Wild static black holes immersed in a magnetic field, which are asymptotic to the Melvin solution. In five spacetime dimensions we define $\beta$ as the least maximal area of all sweepouts of the horizon by two-dimensional tori, and find in all cases examined that $\beta(g) \le \frac{16 \pi}{3} E$, which we conjecture holds quiet generally for apparent horizons. In even spacetime dimensions $D=2N+2$, we find that for sweepouts by the product $S^1 \times S^{D-4}$, $\beta$ is bounded from above by a certain dimension-dependent multiple of the energy $E$. We also find that $\ell^{D-2}$ is bounded from above by a certain dimension-dependent multiple of the horizon area $A$. Finally, we show that $\ell^{D-3}$ is bounded from above by a certain dimension-dependent multiple of the energy, for all Kerr-AdS black holes.Comment: 25 page

Massless Black Holes as Black Diholes and Quadruholes

Massless black holes can be understood as bound states of a (positive mass) extreme a=\sqrt{3} black hole and a singular object with opposite (i.e. negative) mass with vanishing ADM (total) mass but non-vanishing gravitational field. Supersymmetric balance of forces is crucial for the existence of this kind of bound states and explains why the system does not move at the speed of light. We also explain how supersymmetry allows for negative mass as long as it is never isolated but in bound states of total non-negative mass.Comment: Version to be published in Physical Review Letters. Latex2e fil

Are Horned Particles the Climax of Hawking Evaporation?

We investigate the proposal by Callan, Giddings, Harvey and Strominger (CGHS) that two dimensional quantum fluctuations can eliminate the singularities and horizons formed by matter collapsing on the nonsingular extremal black hole of dilaton gravity. We argue that this scenario could in principle resolve all of the paradoxes connected with Hawking evaporation of black holes. However, we show that the generic solution of the model of CGHS is singular. We propose modifications of their model which may allow the scenario to be realized in a consistent manner.Comment: 26 page

Non-Abelian pp-waves in D=4 supergravity theories

The non-Abelian plane waves, first found in flat spacetime by Coleman and subsequently generalized to give pp-waves in Einstein-Yang-Mills theory, are shown to be 1/2 supersymmetric solutions of a wide variety of N=1 supergravity theories coupled to scalar and vector multiplets, including the theory of SU(2) Yang-Mills coupled to an axion \sigma and dilaton \phi recently obtained as the reduction to four-dimensions of the six-dimensional Salam-Sezgin model. In this latter case they provide the most general supersymmetric solution. Passing to the Riemannian formulation of this theory we show that the most general supersymmetric solution may be constructed starting from a self-dual Yang-Mills connection on a self-dual metric and solving a Poisson equation for e^\phi. We also present the generalization of these solutions to non-Abelian AdS pp-waves which allow a negative cosmological constant and preserve 1/4 of supersymmetry.Comment: Latex, 1+12 page

Branes, AdS gravitons and Virasoro symmetry

We consider travelling waves propagating on the anti-de Sitter (AdS) background. It is pointed out that for any dimension d, this space of solutions has a Virasoro symmetry with a non-zero central charge. This result is a natural generalization to higher dimensions of the three-dimensional Brown-Henneaux symmetry.Comment: 4 pages REVTe

The Action of Instantons with Nut Charge

We examine the effect of a non-trivial nut charge on the action of non-compact four-dimensional instantons with a U(1) isometry. If the instanton action is calculated by dimensionally reducing along the isometry, then the nut charge is found to make an explicit non-zero contribution. For metrics satisfying AF, ALF or ALE boundary conditions, the action can be expressed entirely in terms of quantities (including the nut charge) defined on the fixed point set of the isometry. A source (or sink) of nut charge also implies the presence of a Misner string coordinate singularity, which will have an important effect on the Hamiltonian of the instanton.Comment: 25 page

Bohm and Einstein-Sasaki Metrics, Black Holes and Cosmological Event Horizons

We study physical applications of the Bohm metrics, which are infinite sequences of inhomogeneous Einstein metrics on spheres and products of spheres of dimension 5 <= d <= 9. We prove that all the Bohm metrics on S^3 x S^2 and S^3 x S^3 have negative eigenvalue modes of the Lichnerowicz operator and by numerical methods we establish that Bohm metrics on S^5 have negative eigenvalues too. We argue that all the Bohm metrics will have negative modes. These results imply that higher-dimensional black-hole spacetimes where the Bohm metric replaces the usual round sphere metric are classically unstable. We also show that the stability criterion for Freund-Rubin solutions is the same as for black-hole stability, and hence such solutions using Bohm metrics will also be unstable. We consider possible endpoints of the instabilities, and show that all Einstein-Sasaki manifolds give stable solutions. We show how Wick rotation of Bohm metrics gives spacetimes that provide counterexamples to a strict form of the Cosmic Baldness conjecture, but they are still consistent with the intuition behind the cosmic No-Hair conjectures. We show how the Lorentzian metrics may be created ``from nothing'' in a no-boundary setting. We argue that Lorentzian Bohm metrics are unstable to decay to de Sitter spacetime. We also argue that noncompact versions of the Bohm metrics have infinitely many negative Lichernowicz modes, and we conjecture a general relation between Lichnerowicz eigenvalues and non-uniqueness of the Dirichlet problem for Einstein's equations.Comment: 53 pages, 11 figure