1,906 research outputs found
Accelerating expansion and change of signature
We show that some types of sudden singularities admit a natural explanation
in terms of regular changes of signature on brane-worlds in AdS. The
present accelerated expansion of the Universe and its possible ending at a
sudden singularity may therefore simply be an indication that our braneworld is
about to change its Lorentzian signature to an Euclidean one, while remaining
fully regular. An explicit example of this behaviour satisfying the weak and
strong energy conditions is presented.Comment: LaTeX, 4 pages. Uses the eas.cls class. To appear in the proceedings
of the Spanish Relativity Meeting ERE'0
On marginally outer trapped surfaces in stationary and static spacetimes
In this paper we prove that for any spacelike hypersurface containing an
untrapped barrier in a stationary spacetime satisfying the null energy
condition, any marginally outer trapped surface cannot lie in the exterior
region where the stationary Killing vector is timelike. In the static case we
prove that any marginally outer trapped surface cannot penetrate into the
exterior region where the static Killing vector is timelike. In fact, we prove
these result at an initial data level, without even assuming existence of a
spacetime. The proof relies on a powerful theorem by Andersson and Metzger on
existence of an outermost marginally outer trapped surface.Comment: 22 pages, 3 figures; 1 reference added, 1 figure changed, other minor
change
Singularity-Free Cylindrical Cosmological Model
A cylindrically symmetric perfect fluid spacetime with no curvature
singularity is shown. The equation of state for the perfect fluid is that of a
stiff fluid. The metric is diagonal and non-separable in comoving coordinates
for the fluid. It is proven that the spacetime is geodesically complete and
globally hyperbolic.Comment: LaTeX 2e, 8 page
Minimal data at a given point of space for solutions to certain geometric systems
We consider a geometrical system of equations for a three dimensional
Riemannian manifold. This system of equations has been constructed as to
include several physically interesting systems of equations, such as the
stationary Einstein vacuum field equations or harmonic maps coupled to gravity
in three dimensions. We give a characterization of its solutions in a
neighbourhood of a given point through sequences of symmetric trace free
tensors (referred to as `null data'). We show that the null data determine a
formal expansion of the solution and we obtain necessary and sufficient growth
estimates on the null data for the formal expansion to be absolutely convergent
in a neighbourhood of the given point. This provides a complete
characterization of all the solutions to the given system of equations around
that point.Comment: 26 pages, no figure
Is the accelerated expansion evidence of a forthcoming change of signature on the brane?
We show that regular changes of signature on brane-worlds in AdS bulks may
account for some types of the recently fashionable sudden singularities.
Therefore, the possibility that the Universe seems to approach a future sudden
singularity at an accelerated rate of expansion might simply be an indication
that our braneworld is about to change from Lorentzian to Euclidean signature.
Both the brane and the bulk remain fully regular everywhere. We present a model
in which the weak and strong energy conditions hold on the brane, in contrast
with the standard cosmologies leading to the analogous kinematical behaviour
(that is, with a diverging Hubble factor).Comment: 5 pages, 1 figure. Minor improvements in abstract and main text. New
title and new reference added. To be published in PR
Generalisation of the Einstein-Straus model to anisotropic settings
We study the possibility of generalising the Einstein--Straus model to
anisotropic settings, by considering the matching of locally cylindrically
symmetric static regions to the set of on locally rotationally
symmetric (LRS) spacetimes. We show that such matchings preserving the symmetry
are only possible for a restricted subset of the LRS models in which there is
no evolution in one spacelike direction. These results are applied to spatially
homogeneous (Bianchi) exteriors where the static part represents a finite
bounded interior region without holes. We find that it is impossible to embed
finite static strings or other locally cylindrically symmetric static objects
(such as bottle or coin-shaped objects) in reasonable Bianchi cosmological
models, irrespective of the matter content. Furthermore, we find that if the
exterior spacetime is assumed to have a perfect fluid source satisfying the
dominant energy condition, then only a very particular family of LRS stiff
fluid solutions are compatible with this model.
Finally, given the interior/exterior duality in the matching procedure, our
results have the interesting consequence that the Oppenheimer-Snyder model of
collapse cannot be generalised to such anisotropic cases.Comment: LaTeX, 24 pages. Text unchanged. Labels removed from the equations.
Submitted for publicatio
First and Second Order Perturbations of Hypersurfaces
In this paper we find the first and second order perturbations of the induced
metric and the extrinsic curvature of a non-degenerate hypersurface in
a spacetime , when the metric is perturbed arbitrarily to second
order and the hypersurface itself is allowed to change perturbatively (i.e. to
move within spacetime) also to second order. The results are fully general and
hold in arbitrary dimensions and signature. An application of these results for
the perturbed matching theory between spacetimes is presented.Comment: 31 pages, no figures. To be published in Classical and Quantum
Gravit
A classification (uniqueness) theorem for rotating black holes in 4D Einstein-Maxwell-dilaton theory
In the present paper we prove a classification (uniqueness) theorem for
stationary, asymptotically flat black hole spacetimes with connected and
non-degenerate horizon in 4D Einstein-Maxwell-dilaton theory with an arbitrary
dilaton coupling parameter . We show that such black holes are uniquely
specified by the length of the horizon interval, angular momentum, electric and
magnetic charge and the value of the dilaton field at infinity when the dilaton
coupling parameter satisfies . The proof is based on the
nonpositivity of the Riemann curvature operator on the space of the potentials.
A generalization of the classification theorem for spacetimes with disconnected
horizons is also given.Comment: 15 pages, v2 typos correcte
The Wahlquist-Newman solution
Based on a geometrical property which holds both for the Kerr metric and for
the Wahlquist metric we argue that the Kerr metric is a vacuum subcase of the
Wahlquist perfect-fluid solution. The Kerr-Newman metric is a physically
preferred charged generalization of the Kerr metric. We discuss which geometric
property makes this metric so special and claim that a charged generalization
of the Wahlquist metric satisfying a similar property should exist. This is the
Wahlquist-Newman metric, which we present explicitly in this paper. This family
of metrics has eight essential parameters and contains the Kerr-Newman-de
Sitter and the Wahlquist metrics, as well as the whole Pleba\'nski limit of the
rotating C-metric, as particular cases. We describe the basic geometric
properties of the Wahlquist-Newman metric, including the electromagnetic field
and its sources, the static limit of the family and the extension of the
spacetime across the horizon.Comment: LaTeX, 18 pages, no figures. Accepted for publication in Phys. Rev.
Influence of general convective motions on the exterior of isolated rotating bodies in equilibrium
The problem of describing isolated rotating bodies in equilibrium in General
Relativity has so far been treated under the assumption of the circularity
condition in the interior of the body. For a fluid without energy flux, this
condition implies that the fluid flow moves only along the angular direction,
i.e. there is no convection. Using this simplification, some recent studies
have provided us with uniqueness and existence results for asymptotically flat
vacuum exterior fields given the interior sources. Here, the generalisation of
the problem to include general sources is studied. It is proven that the
convective motions have no direct influence on the exterior field, and hence,
that the aforementioned results on uniqueness and existence of exterior fields
apply equally in the general case.Comment: 8 pages, LaTex, uses iopart style files. To appear in Class. Quatum
Gra
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