572 research outputs found
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 of the apparent horizon is shown
to be bounded above in terms of the mass by the , 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 Einstein--Maxwell-dilaton
theory with attractive electric force is found from Einstein--Weyl structures
in (2+1) dimensions corresponding to dispersionless Kadomtsev--Petviashvili and
Toda equations. These solutions are obtained from time--like
Kaluza--Klein reductions of 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 or , 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 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
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 and the total energy is independent of this
parameter.Comment: 8 pages, RevTex, no figure
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