36 research outputs found
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
Variations of the Energy of Free Particles in the pp-Wave Spacetimes
We consider the action of exact plane gravitational waves, or pp-waves, on
free particles. The analysis is carried out by investigating the variations of
the geodesic trajectories of the particles, before and after the passage of the
wave. The initial velocities of the particles are non-vanishing. We evaluate
numerically the Kinetic energy per unit mass of the free particles, and obtain
interesting, quasi-periodic behaviour of the variations of the Kinetic energy
with respect to the width of the gaussian that represents the wave.
The variation of the energy of the free particle is expected to be exactly
minus the variation of the energy of the gravitational field, and therefore
provides an estimation of the local variation of the gravitational energy. The
investigation is carried out in the context of short bursts of gravitational
waves, and of waves described by normalised gaussians, that yield impulsive
waves in a certain limit.Comment: 20 pages, 18 figures, further arguments supporting the localizability
of the gravitational energy are presented, published in Univers
Gravitational pressure on event horizons and thermodynamics in the teleparallel framework
The concept of gravitational pressure is naturally defined in the context of
the teleparallel equivalent of general relativity. Together with the definition
of gravitational energy, we investigate the thermodynamics of rotating black
holes in the teleparallel framework. We obtain the value of the gravitational
pressure over the external event horizon of the Kerr black hole, and write an
expression for the thermodynamic relation , where the variations
refer to the Penrose process for the Kerr black hole. We employ only the
notions of gravitational energy and pressure that arise in teleparallel
gravity, and do not make any consideration of the area or the variation of the
area of the event horizon. However, our results are qualitatively similar to
the standard expression of the literature.Comment: 17 pages, 6 figure