2,384 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
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
G_2 Perfect-Fluid Cosmologies with a proper conformal Killing vector
We study the Einstein field equations for spacetimes admitting a maximal
two-dimensional abelian group of isometries acting orthogonally transitively on
spacelike surfaces and, in addition, with at least one conformal Killing
vector. The three-dimensional conformal group is restricted to the case when
the two-dimensional abelian isometry subalgebra is an ideal and it is also
assumed to act on non-null hypersurfaces (both, spacelike and timelike cases
are studied). We consider both, diagonal and non-diagonal metrics and find all
the perfect-fluid solutions under these assumptions (except those already
known). We find four families of solutions, each one containing arbitrary
parameters for which no differential equations remain to be integrated. We
write the line-elements in a simplified form and perform a detailed study for
each of these solutions, giving the kinematical quantities of the fluid
velocity vector, the energy-density and pressure, values of the parameters for
which the energy conditions are fulfilled everywhere, the Petrov type, the
singularities in the spacetimes and the Friedmann-Lemaitre-Robertson-Walker
metrics contained in each family.Comment: Latex, no figure
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
First order perturbations of the Einstein-Straus and Oppenheimer-Snyder models
We derive the linearly perturbed matching conditions between a Schwarzschild
spacetime region with stationary and axially symmetric perturbations and a FLRW
spacetime with arbitrary perturbations. The matching hypersurface is also
perturbed arbitrarily and, in all cases, the perturbations are decomposed into
scalars using the Hodge operator on the sphere. This allows us to write down
the matching conditions in a compact way. In particular, we find that the
existence of a perturbed (rotating, stationary and vacuum) Schwarzschild cavity
in a perturbed FLRW universe forces the cosmological perturbations to satisfy
constraints that link rotational and gravitational wave perturbations. We also
prove that if the perturbation on the FLRW side vanishes identically, then the
vacuole must be perturbatively static and hence Schwarzschild. By the dual
nature of the problem, the first result translates into links between
rotational and gravitational wave perturbations on a perturbed
Oppenheimer-Snyder model, where the perturbed FLRW dust collapses in a
perturbed Schwarzschild environment which rotates in equilibrium. The second
result implies in particular that no region described by FLRW can be a source
of the Kerr metric.Comment: LaTeX; 29 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
Extremal Isolated Horizons: A Local Uniqueness Theorem
We derive all the axi-symmetric, vacuum and electrovac extremal isolated
horizons. It turns out that for every horizon in this class, the induced metric
tensor, the rotation 1-form potential and the pullback of the electromagnetic
field necessarily coincide with those induced by the monopolar, extremal
Kerr-Newman solution on the event horizon. We also discuss the general case of
a symmetric, extremal isolated horizon. In particular, we analyze the case of a
two-dimensional symmetry group generated by two null vector fields. Its
relevance to the classification of all the symmetric isolated horizons,
including the non-extremal once, is explained.Comment: 22 pages, page size changed, typos and equations (142), (143a)
corrected, PACS number adde
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
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