1,021 research outputs found
Unique characterization of the Bel-Robinson tensor
We prove that a completely symmetric and trace-free rank-4 tensor is, up to
sign, a Bel-Robinson type tensor, i.e., the superenergy tensor of a tensor with
the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a
certain quadratic identity. This may be seen as the first Rainich theory result
for rank-4 tensors.Comment: extended version, 13 pages, shorter version published in
Class.Quant.Gra
Two dimensional Sen connections and quasi-local energy-momentum
The recently constructed two dimensional Sen connection is applied in the
problem of quasi-local energy-momentum in general relativity. First it is shown
that, because of one of the two 2 dimensional Sen--Witten identities, Penrose's
quasi-local charge integral can be expressed as a Nester--Witten integral.Then,
to find the appropriate spinor propagation laws to the Nester--Witten integral,
all the possible first order linear differential operators that can be
constructed only from the irreducible chiral parts of the Sen operator alone
are determined and examined. It is only the holomorphy or anti-holomorphy
operator that can define acceptable propagation laws. The 2 dimensional Sen
connection thus naturally defines a quasi-local energy-momentum, which is
precisely that of Dougan and Mason. Then provided the dominant energy condition
holds and the 2-sphere S is convex we show that the next statements are
equivalent: i. the quasi-local mass (energy-momentum) associated with S is
zero; ii.the Cauchy development is a pp-wave geometry with pure
radiation ( is flat), where is a spacelike hypersurface
whose boundary is S; iii. there exist a Sen--constant spinor field (two spinor
fields) on S. Thus the pp-wave Cauchy developments can be characterized by the
geometry of a two rather than a three dimensional submanifold.Comment: 20 pages, Plain Tex, I
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
Dientes de Abelisauridae y Carcharodontosauridae cf. (Theropoda, Dinosauria) del Campaniano-Maastrichtiano Formación Presidente Prudente (Suroeste Provincia de São Paulo, Brasil)
Isolated theropod teeth referable to Abelisauridae indet., and Carcharodontosauridae cf., from the Campanian-Maastrichtian Presidente Prudente Formation of the western São Paulo State, Brazil, are described. They are compared to the Late Cretaceous Gondwanan theropod dinosaur teeth and their affinities are discussed. These teeth are significant because carnivorous dinosaur remains are poorly known from the Late Cretaceous beds of Western São Paulo State except for a few isolated elements.Se describen dientes aislados de terópodos referidos a Abelisauridae indet. y Carcharodontosauridae cf., procedentes de la Formación Presidente Prudente del Campaniano-Maastrichtiano, en el oeste del estado de San Pablo, Brasil. Los materiales son comparados con dientes de dinosaurios gondwánicos del Cretácico tardío, y cuyas afinidades son aquí discutidas. Estos dientes de dinosaurios carnívoros son significativos debido a que su presencia es pobremente conocida en el Cretácico tardío del oeste del estado del San Pablo, excepto por unos pocos huesos
Two dimensional Sen connections in general relativity
The two dimensional version of the Sen connection for spinors and tensors on
spacelike 2-surfaces is constructed. A complex metric on the spin
spaces is found which characterizes both the algebraic and extrinsic
geometrical properties of the 2-surface . The curvature of the two
dimensional Sen operator is the pull back to of the
anti-self-dual part of the spacetime curvature while its `torsion' is a boost
gauge invariant expression of the extrinsic curvatures of . The difference
of the 2 dimensional Sen and the induced spin connections is the anti-self-dual
part of the `torsion'. The irreducible parts of are shown to be the
familiar 2-surface twistor and the Weyl--Sen--Witten operators. Two Sen--Witten
type identities are derived, the first is an identity between the 2 dimensional
twistor and the Weyl--Sen--Witten operators and the integrand of Penrose's
charge integral, while the second contains the `torsion' as well. For spinor
fields satisfying the 2-surface twistor equation the first reduces to Tod's
formula for the kinematical twistor.Comment: 14 pages, Plain Tex, no report numbe
Dynamical laws of superenergy in General Relativity
The Bel and Bel-Robinson tensors were introduced nearly fifty years ago in an
attempt to generalize to gravitation the energy-momentum tensor of
electromagnetism. This generalization was successful from the mathematical
point of view because these tensors share mathematical properties which are
remarkably similar to those of the energy-momentum tensor of electromagnetism.
However, the physical role of these tensors in General Relativity has remained
obscure and no interpretation has achieved wide acceptance. In principle, they
cannot represent {\em energy} and the term {\em superenergy} has been coined
for the hypothetical physical magnitude lying behind them. In this work we try
to shed light on the true physical meaning of {\em superenergy} by following
the same procedure which enables us to give an interpretation of the
electromagnetic energy. This procedure consists in performing an orthogonal
splitting of the Bel and Bel-Robinson tensors and analysing the different parts
resulting from the splitting. In the electromagnetic case such splitting gives
rise to the electromagnetic {\em energy density}, the Poynting vector and the
electromagnetic stress tensor, each of them having a precise physical
interpretation which is deduced from the {\em dynamical laws} of
electromagnetism (Poynting theorem). The full orthogonal splitting of the Bel
and Bel-Robinson tensors is more complex but, as expected, similarities with
electromagnetism are present. Also the covariant divergence of the Bel tensor
is analogous to the covariant divergence of the electromagnetic energy-momentum
tensor and the orthogonal splitting of the former is found. The ensuing {\em
equations} are to the superenergy what the Poynting theorem is to
electromagnetism. See paper for full abstract.Comment: 27 pages, no figures. Typos corrected, section 9 suppressed and more
acknowledgments added. To appear in Classical and Quantum Gravit
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
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
Conformal Yano-Killing tensor for the Kerr metric and conserved quantities
Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed.
Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime
are obtained from the Yano--Killing tensor. The relation between spin-2 fields
and solutions to the Maxwell equations is used in the construction of a new
conserved quantity which is quadratic in terms of the Weyl tensor. The formula
obtained is similar to the functional obtained from the Bel--Robinson tensor
and is examined in Kerr spacetime. A new interpretation of the conserved
quantity obtained is proposed.Comment: 29 page
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