5 research outputs found
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
Conservation laws for vacuum tetrad gravity
Ten conservation laws in useful polynomial form are derived from a Cartan
form and Exterior Differential System (EDS) for the tetrad equations of vacuum
relativity. The Noether construction of conservation laws for well posed EDS is
introduced first, and an illustration given, deriving 15 conservation laws of
the free field Maxwell Equations from symmetries of its EDS. The Maxwell EDS
and tetrad gravity EDS have parallel structures, with their numbers of
dependent variables, numbers of generating 2-forms and generating 3-forms, and
Cartan character tables all in the ratio of 1 to 4. They have 10 corresponding
symmetries with the same Lorentz algebra, and 10 corresponding conservation
laws.Comment: Final version with additional reference
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
Covariant description of the black hole entropy in 3D gravity
We study the entropy of the black hole with torsion using the covariant form
of the partition function. The regularization of infinities appearing in the
semiclassical calculation is shown to be consistent with the grand canonical
boundary conditions. The correct value for the black hole entropy is obtained
provided the black hole manifold has two boundaries, one at infinity and one at
the horizon. However, one can construct special coordinate systems, in which
the entropy is effectively associated with only one of these boundaries.Comment: 12 pages, LaTeX, v2: new material in section IV clarifies the effects
pertaining to the use of different coordinate system