An extension theorem for conformal gauge singularities

We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.Comment: 43 pages, no figures, version as published in JMP, small changes, updated reference

Collapsing Shells and the Isoperimetric Inequality for Black Holes

Recent results of Trudinger on Isoperimetric Inequalities for non-convex bodies are applied to the gravitational collapse of a lightlike shell of matter to form a black hole. Using some integral identities for co-dimension two surfaces in Minkowski spacetime, the area $A$ of the apparent horizon is shown to be bounded above in terms of the mass $M$ by the $16 \pi G^2 M^2$, which is consistent with the Cosmic Censorship Hypothesis. The results hold in four spacetime dimensions and above.Comment: 16 pages plain TE

Isotropic cosmological singularities: other matter models

Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied (gr-qc/9903008, gr-qc/9903009, gr-qc/9903018) existence and uniqueness of cosmological models with data at the singularity has been established. These were cosmologies with, as source, either perfect fluids with linear equations of state or massless, collisionless particles. In this article we consider how to extend these results to a variety of other matter models. These are scalar fields, massive collisionless matter, the Yang-Mills plasma of Choquet-Bruhat, or matter satisfying the Einstein-Boltzmann equation.Comment: LaTeX, 19 pages, no figure

A comment on Liu and Yau's positive quasi-local mass

Liu and Yau (Phys.Rev.Lett. 90, 231102, 2003) propose a definition of quasi-local mass for any space-like, topological 2-sphere with positive Gauss curvature (and subject to a second, convexity, condition). They are able to show it is positive using a result of Shi and Tam (J.Diff.Geom. 62, 79, 2002). However, as we show here, their definition can give a strictly positive mass for a sphere in flat space

Einstein--Maxwell--Dilaton metrics from three--dimensional Einstein--Weyl structures

A class of time dependent solutions to $(3+1)$ Einstein--Maxwell-dilaton theory with attractive electric force is found from Einstein--Weyl structures in (2+1) dimensions corresponding to dispersionless Kadomtsev--Petviashvili and $SU(\infty)$ Toda equations. These solutions are obtained from time--like Kaluza--Klein reductions of $(3+2)$ solitons.Comment: 12 pages, to be published in Class.Quantum Gra

Einstein-Weyl structures and Bianchi metrics

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally K\"ahler ; in the non-exact Einstein-Weyl case with a Bianchi metric of the type $VII_0, VIII$ or $IX$, we show that the distance may be taken in a diagonal form and we obtain its explicit 4-parameters expression. This extends our previous analysis, limited to the diagonal, K\"ahler Bianchi $IX$ case.Comment: Latex file, 12 pages, a minor modification, accepted for publication in Class. Quant. Gra

Scalar--flat K\"ahler metrics with conformal Bianchi V symmetry

We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b}, and construct all four-dimensional Kahler metrics with vanishing scalar curvature which are invariant under the conformal action of Bianchi V group. The construction is based on the combination of twistor theory and the isomonodromic problem with two double poles. The resulting metrics are non-diagonal in the left-invariant basis and are explicitly given in terms of Bessel functions and their integrals. We also make a connection with the LeBrun ansatz, and characterise the associated solutions of the SU(\infty) Toda equation by the existence a non-abelian two-dimensional group of point symmetries.Comment: Dedicated to Maciej Przanowski on the occasion of his 65th birthday. Minor corrections. To appear in CQ

Energy distribution of charged dilaton black holes

Chamorro and Virbhadra studied, using the energy-momentum complex of Einstein, the energy distribution associated with static spherically symmetric charged dilaton black holes for an arbitrary value of the coupling parameter $\gamma$ which controls the strength of the dilaton to the Maxwell field. We study the same in Tolman's prescription and get the same result as obtained by Chamorro and Virbhadra. The energy distribution of charged dilaton black holes depends on the value of $\gamma$ and the total energy is independent of this parameter.Comment: 8 pages, RevTex, no figure