293 research outputs found
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
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
On the structure of the new electromagnetic conservation laws
New electromagnetic conservation laws have recently been proposed: in the
absence of electromagnetic currents, the trace of the Chevreton superenergy
tensor, is divergence-free in four-dimensional (a) Einstein spacetimes
for test fields, (b) Einstein-Maxwell spacetimes. Subsequently it has been
pointed out, in analogy with flat spaces, that for Einstein spacetimes the
trace of the Chevreton superenergy tensor can be rearranged in the
form of a generalised wave operator acting on the energy momentum
tensor of the test fields, i.e., . In this
letter we show, for Einstein-Maxwell spacetimes in the full non-linear theory,
that, although, the trace of the Chevreton superenergy tensor can
again be rearranged in the form of a generalised wave operator
acting on the electromagnetic energy momentum tensor, in this case the result
is also crucially dependent on Einstein's equations; hence we argue that the
divergence-free property of the tensor has
significant independent content beyond that of the divergence-free property of
Comment on Singularity-free Cosmological Solutions with Non-rotating Perfect Fluids
A conjecture stated by Raychaudhuri which claims that the only physical
perfect fluid non-rotating non-singular cosmological models are comprised in
the Ruiz-Senovilla and Fernandez-Jambrina families is shown to be incorrect. An
explicit counterexample is provided and the failure of the argument leading to
the result is explicitly pointed out.Comment: LaTeX, 5 page
A wide family of singularity-free cosmological models
In this paper a family of non-singular cylindrical perfect fluid cosmologies
is derived. The equation of state corresponds to a stiff fluid. The family
depends on two independent functions under very simple conditions. A sufficient
condition for geodesic completeness is provided.Comment: 7 pages, RevTeX
Stability of marginally outer trapped surfaces and symmetries
We study properties of stable, strictly stable and locally outermost
marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes
possessing certain symmetries such as isometries, homotheties and conformal
Killings. We first obtain results for general diffeomorphisms in terms of the
so-called metric deformation tensor and then particularize to different types
of symmetries. In particular, we find restrictions at the surfaces on the
vector field generating the symmetry. Some consequences are discussed. As an
application we present a result on non-existence of stable marginally outer
trapped surfaces in slices of FLRW.Comment: 23 pages, 3 figure
A local potential for the Weyl tensor in all dimensions
In all dimensions and arbitrary signature, we demonstrate the existence of a
new local potential -- a double (2,3)-form -- for the Weyl curvature tensor,
and more generally for all tensors with the symmetry properties of the Weyl
curvature tensor. The classical four-dimensional Lanczos potential for a Weyl
tensor -- a double (2,1)-form -- is proven to be a particular case of the new
potential: its double dual.Comment: 7 pages; Late
Classification of spacelike surfaces in spacetime
A classification of 2-dimensional surfaces imbedded in spacetime is
presented, according to the algebraic properties of their shape tensor. The
classification has five levels, and provides among other things a refinement of
the concepts of trapped, umbilical and extremal surfaces, which split into
several different classes. The classification raises new important questions
and opens many possible new lines of research. These, together with some
applications and examples, are briefly considered.Comment: 42 pages, 10 tables, many diagram
Axial symmetry and conformal Killing vectors
Axisymmetric spacetimes with a conformal symmetry are studied and it is shown
that, if there is no further conformal symmetry, the axial Killing vector and
the conformal Killing vector must commute. As a direct consequence, in
conformally stationary and axisymmetric spacetimes, no restriction is made by
assuming that the axial symmetry and the conformal timelike symmetry commute.
Furthermore, we prove that in axisymmetric spacetimes with another symmetry
(such as stationary and axisymmetric or cylindrically symmetric spacetimes) and
a conformal symmetry, the commutator of the axial Killing vector with the two
others mush vanish or else the symmetry is larger than that originally
considered. The results are completely general and do not depend on Einstein's
equations or any particular matter content.Comment: 15 pages, Latex, no figure
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