216 research outputs found
A Note on Stress-Tensors, Conservation and Equations of Motion
Some unusual relations between stress tensors, conservation and equations of
motion are briefly reviewed.Comment: 4 pages. Invited contribution, A. Peres Festschrift, to be published
in Found. Phy
A Note on Matter Superenergy Tensors
We consider Bel-Robinson-like higher derivative conserved two-index tensors
H_\mn in simple matter models, following a recently suggested Maxwell field
version. In flat space, we show that they are essentially equivalent to the
true stress-tensors. In curved Ricci-flat backgrounds it is possible to
redefine H_\mn so as to overcome non-commutativity of covariant derivatives,
and maintain conservation, but they become model- and dimension- dependent, and
generally lose their simple "BR" form.Comment: 3 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
Conserved Matter Superenergy Currents for Orthogonally Transitive Abelian G2 Isometry Groups
In a previous paper we showed that the electromagnetic superenergy tensor,
the Chevreton tensor, gives rise to a conserved current when there is a
hypersurface orthogonal Killing vector present. In addition, the current is
proportional to the Killing vector. The aim of this paper is to extend this
result to the case when we have a two-parameter Abelian isometry group that
acts orthogonally transitive on non-null surfaces. It is shown that for
four-dimensional Einstein-Maxwell theory with a source-free electromagnetic
field, the corresponding superenergy currents lie in the orbits of the group
and are conserved. A similar result is also shown to hold for the trace of the
Chevreton tensor and for the Bach tensor, and also in Einstein-Klein-Gordon
theory for the superenergy of the scalar field. This links up well with the
fact that the Bel tensor has these properties and the possibility of
constructing conserved mixed currents between the gravitational field and the
matter fields.Comment: 15 page
On the Energy-Momentum Density of Gravitational Plane Waves
By embedding Einstein's original formulation of GR into a broader context we
show that a dynamic covariant description of gravitational stress-energy
emerges naturally from a variational principle. A tensor is constructed
from a contraction of the Bel tensor with a symmetric covariant second degree
tensor field and has a form analogous to the stress-energy tensor of the
Maxwell field in an arbitrary space-time. For plane-fronted gravitational waves
helicity-2 polarised (graviton) states can be identified carrying non-zero
energy and momentum.Comment: 10 pages, no figure
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
The Chevreton Tensor and Einstein-Maxwell Spacetimes Conformal to Einstein Spaces
In this paper we characterize the source-free Einstein-Maxwell spacetimes
which have a trace-free Chevreton tensor. We show that this is equivalent to
the Chevreton tensor being of pure-radiation type and that it restricts the
spacetimes to Petrov types \textbf{N} or \textbf{O}. We prove that the trace of
the Chevreton tensor is related to the Bach tensor and use this to find all
Einstein-Maxwell spacetimes with a zero cosmological constant that have a
vanishing Bach tensor. Among these spacetimes we then look for those which are
conformal to Einstein spaces. We find that the electromagnetic field and the
Weyl tensor must be aligned, and in the case that the electromagnetic field is
null, the spacetime must be conformally Ricci-flat and all such solutions are
known. In the non-null case, since the general solution is not known on closed
form, we settle with giving the integrability conditions in the general case,
but we do give new explicit examples of Einstein-Maxwell spacetimes that are
conformal to Einstein spaces, and we also find examples where the vanishing of
the Bach tensor does not imply that the spacetime is conformal to a -space.
The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are
conformally -spaces, but none of them are conformal to Einstein spaces.Comment: 22 pages. Corrected equation (12
Multi-site observations of Delta Scuti stars 7 Aql and 8 Aql (a new Delta Scuti variable): The twelfth STEPHI campaign in 2003
We present an analysis of the pulsation behaviour of the Delta Scuti stars 7
Aql (HD 174532) and 8 Aql (HD 174589) -- a new variable star -- observed in the
framework of STEPHI XII campaign during 2003 June--July. 183 hours of high
precision photometry were acquired by using four-channel photometers at three
sites on three continents during 21 days. The light curves and amplitude
spectra were obtained following a classical scheme of multi-channel photometry.
Observations in different filters were also obtained and analyzed. Six and
three frequencies have been unambiguously detected above a 99% confidence level
in the range 0.090 mHz--0.300 mHz and 0.100 mHz-- 0.145 mHz in 7 Aql and 8 Aql
respectively. A comparison of observed and theoretical frequencies shows that 7
Aql and 8 Aql may oscillate with p modes of low radial orders, typical among
Delta Scuti stars. In terms of radial oscillations the range of 8 Aql goes from
n=1 to n=3 while for 7 Aql the range spans from n=4 to n=7. Non-radial
oscillations have to be present in both stars as well. The expected range of
excited modes according to a non adiabatic analysis goes from n=1 to n=6 in
both stars.Comment: 8 pages, 7 fugures, 5 tables, accepted for publication in
Astronomical Journa
Positivity and conservation of superenergy tensors
Two essential properties of energy-momentum tensors T_{\mu\nu} are their
positivity and conservation. This is mathematically formalized by,
respectively, an energy condition, as the dominant energy condition, and the
vanishing of their divergence \nabla^\mu T_{\mu\nu}=0. The classical Bel and
Bel-Robinson superenergy tensors, generated from the Riemann and Weyl tensors,
respectively, are rank-4 tensors. But they share these two properties with
energy momentum tensors: the Dominant Property (DP) and the divergence-free
property in the absence of sources (vacuum). Senovilla defined a universal
algebraic construction which generates a basic superenergy tensor T{A} from any
arbitrary tensor A. In this construction the seed tensor A is structured as an
r-fold multivector, which can always be done. The most important feature of the
basic superenergy tensors is that they satisfy automatically the DP,
independently of the generating tensor A. In a previous paper we presented a
more compact definition of T{A} using the r-fold Clifford algebra. This form
for the superenergy tensors allowed to obtain an easy proof of the DP valid for
any dimension. In this paper we include this proof. We explain which new
elements appear when we consider the tensor T{A} generated by a
non-degree-defined r-fold multivector A and how orthogonal Lorentz
transformations and bilinear observables of spinor fields are included as
particular cases of superenergy tensors. We find some sufficient conditions for
the seed tensor A, which guarantee that the generated tensor T{A} is
divergence-free. These sufficient conditions are satisfied by some physical
fields, which are presented as examples.Comment: 19 pages, no figures. Language and minor changes. Published versio
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