814 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
On reference frames in spacetime and gravitational energy in freely falling frames
We consider the interpretation of tetrad fields as reference frames in
spacetime. Reference frames may be characterized by an antisymmetric
acceleration tensor, whose components are identified as the inertial
accelerations of the frame (the translational acceleration and the frequency of
rotation of the frame). This tensor is closely related to
gravitoelectromagnetic field quantities. We construct the set of tetrad fields
adapted to observers that are in free fall in the Schwarzschild spacetime, and
show that the gravitational energy-momentum constructed out of this set of
tetrad fields, in the framework of the teleparallel equivalent of general
relatrivity, vanishes. This result is in agreement with the principle of
equivalence, and may be taken as a condition for a viable definition of
gravitational energy.Comment: 19 pages, no figures, accepted by Classical and Quantum Gravit
Gravitational energy of rotating black holes
In the teleparallel equivalent of general relativity the energy density of
asymptotically flat gravitational fields can be naturaly defined as a scalar
density restricted to a three-dimensional spacelike hypersurface .
Integration over the whole yields the standard ADM energy. After
establishing the reference space with zero gravitational energy we obtain the
expression of the localized energy for a Kerr black hole. The expression of the
energy inside a surface of constant radius can be explicitly calculated in the
limit of small , the specific angular momentum. Such expression turns out to
be exactly the same as the one obtained by means of the method preposed
recently by Brown and York. We also calculate the energy contained within the
outer horizon of the black hole for {\it any} value of . The result is
practically indistinguishable from , where is the
irreducible mass of the black hole.Comment: 18 pages, LaTex file, one figur
Hamiltonian formulation of general relativity in the teleparallel geometry
We establish the Hamiltonian formulation of the teleparallel equivalent of
general relativity, without fixing the time gauge condition, by rigorously
performing the Legendre transform. The time gauge condition, previously
considered, restricts the teleparallel geometry to the three-dimensional
spacelike hypersurface. Geometrically, the teleparallel geometry is now
extended to the four-dimensional space-time. The resulting Hamiltonian
formulation is different from the standard ADM formulation in many aspects, the
main one being that the dynamics is now governed by the Hamiltonian constraint
H_0 and a set of primary constraints. The vector constraint H_i is derived from
the Hamiltonian constraint. The vanishing of the latter implies the vanishing
of the vector constraint.Comment: 22 pages, Latex file, no figures. The title has been changed. The
complete constraint algebra is presented. The derivation of the vector
constraint from the Hamiltonian constraint is presented with further details.
Version to appear in the PR
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
The gravitational energy-momentum flux
We present a continuity equation for the gravitational energy-momentum, which
is obtained in the framework of the teleparallel equivalent of general
relativity. From this equation it follows a general definition for the
gravitational energy-momentum flux. This definition is investigated in the
context of plane waves and of cylindrical Einstein-Rosen waves. We obtain the
well known value for the energy flux of plane gravitational waves, and conclude
that the latter exhibit features similar to plane electromagnetic waves.Comment: 20 pages, latex file, no figures, two references added, accepted for
publication in Class. Quantum Gravit
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