4,324 research outputs found
Regularized expression for the gravitational energy-momentum in teleparallel gravity and the principle of equivalence
The expression of the gravitational energy-momentum defined in the context of
the teleparallel equivalent of general relativity is extended to an arbitrary
set of real-valued tetrad fields, by adding a suitable reference space
subtraction term. The characterization of tetrad fields as reference frames is
addressed in the context of the Kerr space-time. It is also pointed out that
Einstein's version of the principle of equivalence does not preclude the
existence of a definition for the gravitational energy-momentum density.Comment: 17 pages, Latex file, no figure; minor correction in eq. (14), three
references added, to appear in the GRG Journa
Sparling two-forms, the conformal factor and the gravitational energy density of the teleparallel equivalent of general relativity
It has been shown recently that within the framework of the teleparallel
equivalent of general relativity (TEGR) it is possible to define the energy
density of the gravitational field. The TEGR amounts to an alternative
formulation of Einstein's general relativity, not to an alternative gravity
theory. The localizability of the gravitational energy has been investigated in
a number of space-times with distinct topologies, and the outcome of these
analises agree with previously known results regarding the exact expression of
the gravitational energy, and/or with the specific properties of the space-time
manifold. In this article we establish a relationship between the expression
for the gravitational energy density of the TEGR and the Sparling two-forms,
which are known to be closely connected with the gravitational energy. We also
show that our expression of energy yields the correct value of gravitational
mass contained in the conformal factor of the metric field.Comment: 12 pages, Latex file, no figures, to be published in Gen. Rel. Gra
The Teleparallel Equivalent of General Relativity and the Gravitational Centre of Mass
We present a brief review of the teleparallel equivalent of general
relativity and analyse the expression for the centre of mass density of the
gravitational field. This expression has not been sufficiently discussed in the
literature. One motivation for the present analysis is the investigation of the
localization of dark energy in the three-dimensional space, induced by a
cosmological constant in a simple Schwarzschild-de Sitter space-time. We also
investigate the gravitational centre of mass density in a particular model of
dark matter, in the space-time of a point massive particle and in an arbitrary
space-time with axial symmetry. The results are plausible, and lead to the
notion of gravitational centre of mass (COM) distribution function.Comment: 22 pages, no figures, the title has been changed, references added,
published in Universe (100 Years of Chronogeometrodynamics: the Status of the
Einstein's Theory of Gravitation in Its Centennial Year
Electrodynamics in accelerated frames revisited
Maxwell's equations are formulated in arbitrary moving frames by means of
tetrad fields, which are interpreted as reference frames adapted to observers
in space-time. We assume the existence of a general distribution of charges and
currents in an inertial frame. Tetrad fields are used to project the
electromagnetic fields and sources on accelerated frames. The purpose is to
study several configurations of fields and observers that in the literature are
understood as paradoxes. For instance, are the two situations, (i) an
accelerated charge in an inertial frame, and (ii) a charge at rest in an
inertial frame described from the perspective of an accelerated frame,
physically equivalent? Is the electromagnetic radiation the same in both
frames? Normally in the analysis of these paradoxes the electromagnetic fields
are transformed to (uniformly) accelerated frames by means of a coordinate
transformation of the Faraday tensor. In the present approach coordinate and
frame transformations are disentangled, and the electromagnetic field in the
accelerated frame is obtained through a frame (local Lorentz) transformation.
Consequently the fields in the inertial and accelerated frames are described in
the same coordinate system. This feature allows the investigation of paradoxes
such as the one mentioned above.Comment: 17 pages, no figure
Gravitational energy of a magnetized Schwarzschild black hole - a teleparallel approach
We investigate the distribution of gravitational energy on the spacetime of a
Schwarzschild black hole immersed in a cosmic magnetic field. This is done in
the context of the {\it Teleparallel Equivalent of General Relativity}, which
is an alternative geometrical formulation of General Relativity, where gravity
is describe by a spacetime endowed with torsion, rather than curvature, with
the fundamental field variables being tetrads. We calculate the energy enclosed
by a two-surface of constant radius - in particular, the energy enclosed by the
event horizon of the black hole. In this case we find that the magnetic field
has the effect of increasing the gravitational energy as compared to the vacuum
Schwarzschild case. We also compute the energy (i) in the weak magnetic field
limit, (ii) in the limit of vanishing magnetic field, and (iii) in the absence
of the black hole. In all cases our results are consistent with what should be
expected on physical grounds.Comment: version to match the one to be published on General Relativity and
Gravitatio
Teleparallel gauge theory of gravity
In this work a tetrad theory of gravity, invariant under conformal
transformations, is investigated. The action of the theory is similar to the
action of Maxwell's electromagnetism. The role of the electromagnetic gauge
potential is played by the trace of the torsion tensor of the Weitzenb\"ock
spacetime. It is shown that all static, spherically symmetric space-times, are
solutions of the vacuum field equations. However, by fixing the gauge in the
linearized form of the vacuum field equations, the usual Newtonian limit for
the gravitational field is obtained.Comment: 10 pages, no figures, 5 references adde
Neutron Stars in Teleparallel Gravity
In this paper we deal with neutron stars, which are described by a perfect
fluid model, in the context of the teleparallel equivalent of general
relativity. We use numerical simulations to find the relationship between the
angular momentum of the field and the angular momentum of the source. Such a
relation was established for each stable star reached by the numerical
simulation once the code is fed with an equation of state, the central energy
density and the ratio between polar and equatorial radii. We also find a regime
where linear relation between gravitational angular momentum and moment of
inertia (as well as angular velocity of the fluid) is valid. We give the
spatial distribution of the gravitational energy and show that it has a linear
dependence with the squared angular velocity of the source.Comment: 19 pages, 14 figures. arXiv admin note: text overlap with
arXiv:1206.331
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