3,729 research outputs found
Extreme objects with arbitrary large mass, or density, and arbitrary size
We consider a generalization of the interior Schwarzschild solution that we
match to the exterior one to build global C^1 models that can have arbitrary
large mass, or density, with arbitrary size. This is possible because of a new
insight into the problem of localizing the center of symmetry of the models and
the use of principal transformations to understand the structure of space.Comment: 20 pages, 6 figures. Fixed one reference. Added a new equatio
Grid-scale Fluctuations and Forecast Error in Wind Power
The fluctuations in wind power entering an electrical grid (Irish grid) were
analyzed and found to exhibit correlated fluctuations with a self-similar
structure, a signature of large-scale correlations in atmospheric turbulence.
The statistical structure of temporal correlations for fluctuations in
generated and forecast time series was used to quantify two types of forecast
error: a timescale error () that quantifies the deviations between
the high frequency components of the forecast and the generated time series,
and a scaling error () that quantifies the degree to which the
models fail to predict temporal correlations in the fluctuations of the
generated power. With no knowledge of the forecast models, we
suggest a simple memory kernel that reduces both the timescale error
() and the scaling error ()
Comparing metrics at large: harmonic vs quo-harmonic coordinates
To compare two space-times on large domains, and in particular the global
structure of their manifolds, requires using identical frames of reference and
associated coordinate conditions. In this paper we use and compare two classes
of time-like congruences and corresponding adapted coordinates: the harmonic
and quo-harmonic classes. Besides the intrinsic definition and some of their
intrinsic properties and differences we consider with some detail their
differences at the level of the linearized approximation of the field
equations. The hard part of this paper is an explicit and general determination
of the harmonic and quo-harmonic coordinates adapted to the stationary
character of three well-know metrics, Schwarzschild's, Curzon's and Kerr's, to
order five of their asymptotic expansions. It also contains some relevant
remarks on such problems as defining the multipoles of vacuum solutions or
matching interior and exterior solutions.Comment: 27 pages, no figure
Energy and Momentum Distributions of a (2+1)-dimensional black hole background
Using Einstein, Landau-Lifshitz, Papapetrou and Weinberg energy-momentum
complexes we explicitly evaluate the energy and momentum distributions
associated with a non-static and circularly symmetric three-dimensional
spacetime. The gravitational background under study is an exact solution of the
Einstein's equations in the presence of a cosmological constant and a null
fluid. It can be regarded as the three-dimensional analogue of the Vaidya
metric and represents a non-static spinless (2+1)-dimensional black hole with
an outflux of null radiation. All four above-mentioned prescriptions give
exactly the same energy and momentum distributions for the specific black hole
background. Therefore, the results obtained here provide evidence in support of
the claim that for a given gravitational background, different energy-momentum
complexes can give identical results in three dimensions. Furthermore, in the
limit of zero cosmological constant the results presented here reproduce the
results obtained by Virbhadra who utilized the Landau-Lifshitz energy-momentum
complex for the same (2+1)-dimensional black hole background in the absence of
a cosmological constant.Comment: 19 pages, LaTeX, v3: references added, to appear in Int.J.Mod.Phys.
Bel-Robinson tensor and dominant energy property in the Bianchi type I Universe
Within the framework of Bianchi type-I space-time we study the Bel-Robinson
tensor and its impact on the evolution of the Universe. We use different
definitions of the Bel-Robinson tensor existing in the literature and compare
the results. Finally we investigate the so called "dominant super-energy
property" for the Bel-Robinson tensor as a generalization of the usual dominant
energy condition for energy momentum tensors.
Keywords: Bianchi type I model, super-energy tensors
Pacs: 03.65.Pm and 04.20.HaComment: 15 pages, revised version, 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
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
f-symbols, Killing tensors and conserved Bel-type currents
In the framework of the General Relativity we show that from three
generalizations of Killing vector fields, namely f-symbols, symmetric
St\"{a}ckel-Killing and antisymmetric Killing-Yano tensors, some conserved
currents can be obtained through adequate contractions of the above mentioned
objects with rank four tensors having the properties of Bel or Bel-Robinson
tensors in Einstein spaces.Comment: 13 pages, accepted for publication in Mod. Phys. Lett.
Conserved superenergy currents
We exploit once again the analogy between the energy-momentum tensor and the
so-called ``superenergy'' tensors in order to build conserved currents in the
presence of Killing vectors. First of all, we derive the divergence-free
property of the gravitational superenergy currents under very general
circumstances, even if the superenergy tensor is not divergence-free itself.
The associated conserved quantities are explicitly computed for the
Reissner-Nordstrom and Schwarzschild solutions. The remaining cases, when the
above currents are not conserved, lead to the possibility of an interchange of
some superenergy quantities between the gravitational and other physical fields
in such a manner that the total, mixed, current may be conserved. Actually,
this possibility has been recently proved to hold for the Einstein-Klein-Gordon
system of field equations. By using an adequate family of known exact
solutions, we present explicit and completely non-obvious examples of such
mixed conserved currents.Comment: LaTeX, 19 pages; improved version adding new content to the second
section and some minor correction
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