946 research outputs found
Slowly rotating charged fluid balls and their matching to an exterior domain
The slow-rotation approximation of Hartle is developed to a setting where a
charged rotating fluid is present. The linearized Einstein-Maxwell equations
are solved on the background of the Reissner-Nordstrom space-time in the
exterior electrovacuum region. The theory is put to action for the charged
generalization of the Wahlquist solution found by Garcia. The Garcia solution
is transformed to coordinates suitable for the matching and expanded in powers
of the angular velocity. The two domains are then matched along the zero
pressure surface using the Darmois-Israel procedure. We prove a theorem to the
effect that the exterior region is asymptotically flat if and only if the
parameter C_{2}, characterizing the magnitude of an external magnetic field,
vanishes. We obtain the form of the constant C_{2} for the Garcia solution. We
conjecture that the Garcia metric cannot be matched to an asymptotically flat
exterior electrovacuum region even to first order in the angular velocity. This
conjecture is supported by a high precision numerical analysis.Comment: 11 pages, 2 figure
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
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
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
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
Symmetry-preserving matchings
In the literature, the matchings between spacetimes have been most of the
times implicitly assumed to preserve some of the symmetries of the problem
involved. But no definition for this kind of matching was given until recently.
Loosely speaking, the matching hypersurface is restricted to be tangent to the
orbits of a desired local group of symmetries admitted at both sides of the
matching and thus admitted by the whole matched spacetime. This general
definition is shown to lead to conditions on the properties of the preserved
groups. First, the algebraic type of the preserved group must be kept at both
sides of the matching hypersurface. Secondly, the orthogonal transivity of
two-dimensional conformal (in particular isometry) groups is shown to be
preserved (in a way made precise below) on the matching hypersurface. This
result has in particular direct implications on the studies of axially
symmetric isolated bodies in equilibrium in General Relativity, by making up
the first condition that determines the suitability of convective interiors to
be matched to vacuum exteriors. The definition and most of the results
presented in this paper do not depend on the dimension of the manifolds
involved nor the signature of the metric, and their applicability to other
situations and other higher dimensional theories is manifest.Comment: LaTeX, 19 page
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
On Uniqueness of static Einstein-Maxwell-Dilation black holes
We prove uniqueness of static, asymptotically flat spacetimes with non-degenerate black holes for three special cases of Einstein-Maxwell-dilaton theory: For the coupling '''''' (which is the low energy limit of string theory) on the one hand, and for vanishing magnetic or vanishing electric field (but arbitrary coupling) on the other hand. Our work generalizes in a natural, but non-trivial way the uniqueness result obtained by Masood-ul-Alam who requires both and absence of magnetic fields, as well as relations between the mass and the charges. Moreover, we simplify Masood-ul-Alam's proof as we do not require any non-trivial extensions of Witten's positive mass theorem. We also obtain partial results on the uniqueness problem for general harmonic m
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.
Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order
Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by
a matter-filled interior and an asymptotically flat vacuum exterior joined at a
surface where the Darmois matching conditions are satisfied, are considered.
The initial state is assumed to be static. The perturbations of the matching
conditions are derived and used as boundary conditions for the perturbed Ernst
equations in the exterior region. The perturbations are calculated to second
order. The boundary conditions are overdetermined: necessary and sufficient
conditions for their compatibility are derived. The special case of
perturbations of spherical bodies is given in detail.Comment: RevTeX; 32 pp. Accepted by Phys. Rev. D. Added references and extra
comments in introductio
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