351 research outputs found
On the construction of global models describing rotating bodies; uniqueness of the exterior gravitational field
The problem of constructing global models describing isolated axially
symmetric rotating bodies in equilibrium is analyzed. It is claimed that,
whenever the global spacetime is constructed by giving boundary data on the
limiting surface of the body and integrating Einstein's equations both inside
and ouside the body, the problem becomes overdetermined. Similarly, when the
spacetime describing the interior of the body is explicitly given,the problem
of finding the exterior vacuum solution becomes overdetermined. We discuss in
detail the procedure to be followed in order to construct the exterior vacuum
field created by a given but arbitrary distribution of matter. Finally, the
uniqueness of the exterior vacuum gravitational field is proven by exploiting
the harmonic map formulation of the vacuum equations and the boundary
conditions prescribed from the matching.Comment: Latex, 10 pages, no figure
Investigation of all Ricci semi-symmetric and all conformally semi-symmetric spacetimes
We find all Ricci semi-symmetric as well as all conformally semi-symmetric
spacetimes. Neither of these properties implies the other. We verify that only
conformally flat spacetimes can be Ricci semi-symmetric without being
conformally semi-symmetric and show that only vacuum spacetimes and spacetimes
with just a -term can be Ricci semi-symmetric without being
conformally semi-symmetric.Comment: 4 pages, 1 tabl
Singularity theorems based on trapped submanifolds of arbitrary co-dimension
Standard singularity theorems are proven in Lorentzian manifolds of arbitrary
dimension n if they contain closed trapped submanifolds of arbitrary
co-dimension. By using the mean curvature vector to characterize trapped
submanifolds, a unification of the several possibilities for the boundary
conditions in the traditional theorems and their generalization to arbitrary
co-dimension is achieved. The classical convergence conditions must be replaced
by a condition on sectional curvatures, or tidal forces, which reduces to the
former in the cases of co-dimension 1, 2 or n.Comment: 11 pages, no figures, some corrections
A singularity-free space-time
We show that the solution published in Ref.1 is geodesically complete and
singularity-free. We also prove that the solution satisfies the stronger energy
and causality conditions, such as global hyperbolicity, causal symmetry and
causal stability. A detailed discussion about which assumptions in the
singularity theorems are not fulfilled is performed, and we show explicitly
that the solution is in accordance with those theorems. A brief discussion of
the results is given.Comment: Latex 2.09, 14 page
Conserved Matter Superenergy Currents for Hypersurface Orthogonal Killing Vectors
We show that for hypersurface orthogonal Killing vectors, the corresponding
Chevreton superenergy currents will be conserved and proportional to the
Killing vectors. This holds for four-dimensional Einstein-Maxwell spacetimes
with an electromagnetic field that is sourcefree and inherits the symmetry of
the spacetime. A similar result also holds for the trace of the Chevreton
tensor. The corresponding Bel currents have previously been proven to be
conserved and our result can be seen as giving further support to the concept
of conserved mixed superenergy currents. The analogous case for a scalar field
has also previously been proven to give conserved currents and we show, for
completeness, that these currents also are proportional to the Killing vectors.Comment: 13 page
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