574 research outputs found
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
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
Localization of Energy in General Relativity
In the framework of the teleparallel equivalent of general relativity the
energy density of asymptoticaly flat gravitational fields can be naturally and
unambiguously defined. Upon integration of the energy density over the whole
three dimensional space we obtain the ADM energy. We use this energy density to
calculate the energy inside a Schwarzschild black hole.Comment: 12 pages, LaTex file, no figure
Gravitational energy of conical defects
The energy density of asymptotically flat gravitational fields can be
calculated from a simple expression involving the trace of the torsion tensor.
Integration of this energy density over the whole space yields the ADM energy.
Such expression can be justified within the framework of the teleparallel
equivalent of general relativity, which is an alternative geometrical
formulation of Einstein's general relativity. In this paper we apply this
energy density to the evaluation of the energy per unit length of a class of
conical defects of topological nature, which include disclinations and
dislocations (in the terminology of crystallography). Disclinations correspond
to cosmic strings, and for a spacetime endowed with only such a defect we
obtain precisely the well known expression of energy per unit length. However
for a pure spacetime dislocation the total gravitational energy is zero.Comment: 16 pages, LaTex file, no figure, additional text included, to appear
in the J. Math. Phy
Canonical Formulation of Gravitational Teleparallelism in 2+1 Dimensions in Schwinger's Time Gauge
We consider the most general class of teleparallel gravitational {}{}theories
quadratic in the torsion tensor, in three space-time dimensions, and carry out
a detailed investigation of its Hamiltonian formulation in Schwinger's time
gauge. This general class is given by a family of three-parameter theories. A
consistent implementation of the Legendre transform reduces the original theory
to a one-parameter family of theories. By calculating Poisson brackets we show
explicitly that the constraints of the theory constitute a first-class set.
Therefore the resulting theory is well defined with regard to time evolution.
The structure of the Hamiltonian theory rules out the existence of the
Newtonian limit.Comment: 17 pages, Latex file, no figures; a numerical coefficient has been
corrected and a different result is achieve
Black Holes in 2+1 Teleparallel Theories of Gravity
We apply the Hamiltonian formulation of teleparallel theories of gravity in
2+1 dimensions to a circularly symmetric geometry. We find a family of
one-parameter black hole solutions. The BTZ solution fixes the unique free
parameter of the theory. The resulting field equations coincide with the
teleparallel equivalent of Einstein's three-dimensional equations. We calculate
the gravitational energy of the black holes by means of the simple expression
that arises in the Hamiltonian formulation and conclude that the resulting
value is identical to that calculated by means of the Brown-York method.Comment: 20 pages, Latex file, no figure
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