59 research outputs found
Algebraic Rainich theory and antisymmetrisation in higher dimensions
The classical Rainich(-Misner-Wheeler) theory gives necessary and sufficient
conditions on an energy-momentum tensor to be that of a Maxwell field (a
2-form) in four dimensions. Via Einstein's equations these conditions can be
expressed in terms of the Ricci tensor, thus providing conditions on a
spacetime geometry for it to be an Einstein-Maxwell spacetime. One of the
conditions is that is proportional to the metric, and it has previously
been shown in arbitrary dimension that any tensor satisfying this condition is
a superenergy tensor of a simple -form. Here we examine algebraic Rainich
conditions for general -forms in higher dimensions and their relations to
identities by antisymmetrisation. Using antisymmetrisation techniques we find
new identities for superenergy tensors of these general (non-simple) forms, and
we also prove in some cases the converse; that the identities are sufficient to
determine the form. As an example we obtain the complete generalisation of the
classical Rainich theory to five dimensions.Comment: 16 pages, LaTe
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
Flat deformation of a spacetime admitting two Killing fields
It is shown that given an analytic Lorentzian metric on a 4-manifold, ,
which admits two Killing vector fields, then it exists a local deformation law
, where is a 2-dimensional projector, such that is
flat and admits the same Killing vectors. We also characterize the particular
case when the projector coincides with the quotient metric. We apply some
of our results to general stationary axisymmetric spacetime
Form Geometry and the 'tHooft-Plebanski Action
Riemannian geometry in four dimensions, including Einstein's equations, can
be described by means of a connection that annihilates a triad of two-forms
(rather than a tetrad of vector fields). Our treatment of the conformal factor
of the metric differs from the original presentation of this result, due to
'tHooft. In the action the conformal factor now appears as a field to be
varied.Comment: 12pp, LaTe
A new duality transformation for fourth-order gravity
We prove that for non-linear L = L(R), the Lagrangians L and \hat L give
conformally equivalent fourth-order field equations being dual to each other.
The proof represents a new application of the fact that the operator
is conformally invariant.Comment: 11 pages, LaTeX, no figures. Gen. Relat. Grav. in prin
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
Obtaining the Weyl tensor from the Bel-Robinson tensor
The algebraic study of the Bel-Robinson tensor proposed and initiated in a
previous work (Gen. Relativ. Gravit. {\bf 41}, see ref [11]) is achieved. The
canonical form of the different algebraic types is obtained in terms of
Bel-Robinson eigen-tensors. An algorithmic determination of the Weyl tensor
from the Bel-Robinson tensor is presented.Comment: 21 page
Rainich theory for type D aligned Einstein-Maxwell solutions
The original Rainich theory for the non-null Einstein-Maxwell solutions
consists of a set of algebraic conditions and the Rainich (differential)
equation. We show here that the subclass of type D aligned solutions can be
characterized just by algebraic restrictions.Comment: 12 pages; v2: appendix with notatio
Dimensionally Dependent Tensor Identities by Double Antisymmetrisation
Some years ago, Lovelock showed that a number of apparently unrelated
familiar tensor identities had a common structure, and could all be considered
consequences in n-dimensional space of a pair of fundamental identities
involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's
results, and by using the fact that associated with any tensor in n-dimensional
space there is associated a fundamental tensor identity obtained by
antisymmetrising over n+1 indices, we establish a very general 'master'
identity for all trace-free (k,l)-forms. We then show how various other special
identities are direct and simple consequences of this master identity; in
particular we give direct application to Maxwell, Lanczos, Ricci, Bel and
Bel-Robinson tensors, and also demonstrate how relationships between scalar
invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure
Scaling of Aharonov-Bohm couplings and the dynamical vacuum in gauge theories
Recent results on the vacuum polarization induced by a thin string of
magnetic flux lead us to suggest an analogue of the Copenhagen `flux spaghetti'
QCD vacuum as a possible mechanism for avoiding the divergence of perturbative
QED, thus permitting consistent completion of the full, nonperturbative theory.
The mechanism appears to operate for spinor, but not scalar, QED.Comment: 11 pages, ITP-SB-92-40, (major conceptual evolution from original
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