1,335 research outputs found
The modification of the Einstein and Landau-Lifshitz pseudotensrs
Deser et al. proposed a combination of the Einstein and Landau-Lifshitz
pseudotensors such that the second derivatives in vacuum are proportional to
the Bel-Robinson tensor. Stimulated by their work, the present paper discuss
the gravitational energy-momentum expression which has the same desirable
Bel-Robinson tensor property. We find modifications of the Einstein and
Landau-Lifshitz pseudotensors that both give the same coefficient of the
Bel-Robinson tensor in vacuum in holonomic frames.Comment: 10 page
Modification of the Bel-Robinson type energy-momentum
For describing the non-negative gravitational energy-momentum in terms of a
pure Bel-Robinson type energy-momentum in a quasilocal 2-surface, both the
Bel-Robinson tensor and tensor are suitable. We found that this
Bel-Robinson type energy-momentum can be modified such that it satisfies the
Lorentz covariant, future pointing and non-spacelike properties. We find that
these particular energy-momentum properties can be obtained from (i): or
plus a tensor in a quasilocal small cube limit, or (ii): directly
evaluating the energy-momentum of or in a quasilocal small box region.Comment: 6 page
General relativistic tidal heating for Moller pseudotensor
Thorne elucidated that the relativistic tidal heating is the same as the
Newtonian theory. Moreover, Thorne also claimed that the tidal heating is
independent of how one localizes gravitational energy and is unambiguously
given by a certain formula. Purdue and Favata calculated the tidal heating for
different classical pseudotensors including Moller and obtained the results all
matched with the Newtonian perspective. After re-examined this Moller
pseudotensor, we find that there does not exist any tidal heating value. Thus
we claim that the relativistic tidal heating is pseudotensor independent under
the condition that if the peusdotensor is a Freud typed superpotential.Comment: 4 page
General relativistic tidal work for Papapetrou, Weinberg and Goldberg pseudotensors
In 1998 Thorne claimed that all pseudotensors give the same tidal work as the
Newtonian theory. In 1999, Purdue used the Landau-Lifshitz pseudotensor to
calculate the tidal heating and the result matched with the Newtonian gravity.
Soon after in 2001, Favata employed the same method to examine the Einstein,
Bergmann-Thomson and M{\o}ller pseudotensors, all of them give the same result
as Purdue did. Inspired by the work of Purdue and Favata, for the completeness,
here we manipulate the tidal work for Papapetrou, Weinberg and Goldberg
pseudotensors. We obtained the same tidal work as Purdue achieved. In addition,
we emphasize that a suitable gravitational energy-momentum pseudotensor
requires fulfill the inside matter condition and all of the classical
pseudotensors pass this test except M\oller. Moreover, we constructed a
general pseudotesnor which is modified by 13 linear artificial higher order
terms combination with Einstein pseudotensor. We find that the result agrees
with Thorne's prediction, i.e., relativistic tidal work is pseudotensor
independent.Comment: 6 page
General relativistic tidal heating for the Moller pseudotensor
In his study of tidal stabilization of fully relativistic neutron stars
Thorne showed that the fully relativistic expression for tidal heating is the
same as in non-relativistic Newtonian theory. Furthermore, Thorne also noted
that the tidal heating must be independent of how one localizes gravitational
energy and is unambiguously given by that expression. Purdue and Favata
calculated the tidal heating for a number of classical gravitational
pseudotensors including that of Moller, and obtained the result that all of
them produced the same (Newtonian) value. However, in a re-examination of the
calculation using the Moller pseudotensor we find that there is no tidal
heating. This leads us to the conclusion that Thorne's assertion needs a minor
modification: the relativistic tidal heating is pseudotensor independent only
if the pseudotensor is derived from a Freud type superpotential.Comment: 10 pages, a major revision of arXiv:1509.0920
Relativistic tidal heating of Hamiltonian quasi-local boundary expressions
Purdue and Favata calculate the tidal heating used certain classical
pseudotensors. Booth and Creighton employed the quasi-local mass formalism of
Brown and York to demonstrate the same subject. All of them give the result
matched with the Newtonian theory. Here we present another Hamiltonian
quasi-local boundary expressions and all give the same desired value. This
indicates that the tidal heating is unique as Thorne predicted. Moreover, we
discovered that the pseudo-tensor method and quasi-local method are
fundamentally different.Comment: 6 page
Gravitational energy in small regions for the quasilocal expressions in orthonormal frames
The M\oller tetrad gravitational energy-momentum expression was recently
evaluated for a small vacuum region using orthonormal frames adapted to Riemann
normal coordinates. However the result was not proportional to the Bel-Robinson
tensor . Treating a modified quasilocal expressions in a
similar way, we found one unique combination that gives a multiple of
which provides a non-negative gravitational
energy-momentum in the small sphere approximation. Moreover, in addition to
, we found a certain tensor
which gives the same
"energy-momentum" density in vacuum. Using this tensor combination, we obtained
an infinite set of solutions that provides a positive gravitational energy
within the same limit.Comment:
Application of the 3-space approach to the Bianchi II cosmological model
Einstein used 4-dimensional space time geometry to explain gravity. However,
in 1962, Baierlein, Sharp and Wheeler proposed a Jacobi type timeless
Lagrangian based on the 3-dimensional geometry of space to reproduce the same
physics. In 2002, Barbour . . further extended this idea and they call
it 3-space approach. Here we use Bianchi II cosmological model to demonstrate
the 3-space idea. Indeed, we find that this theory is more fundamental and the
manipulation is more practical. We recover the known and find a new solutions.Comment: 5 page
Quasilocal energy-momentum for tensor V in small regions
The Bel-Robinson tensor and the tensor have the same quasilocal
energy-momentum in a small sphere. Using a pseudotensor approach to evaluate
the energy-momentum in a half-cylinder, we find that and have different
values, not proportional to the `Bel-Robinson energy-momentum'. Furthermore,
even if we arrange things so that we do get the same `Bel-Robinson
energy-momentum' value, the angular momentum gives different values using
and in half-cylinder. In addition, we find that and have a
different number of independent components. The fully trace free property of
and implies conservation of pure `Bel-Robinson energy-momentum' in
small regions, and vice versa.Comment: 8 pages, a major revision of arXiv:1006.527
Gravitational energy-momentum in small regions according to the tetrad-teleparallel expressions
The gravitational energy-momentum within a small region as determined by two
tetrad-teleparallel expressions is evaluated with the aid of an orthonormal
frame adapted to Riemann normal coordinates. We find that the gauge current
"tensor" does enjoy the highly desired and rare property of being a positive
multiple of the Bel-Robinson tensor, whereas M{\o}ller's expression does not.Comment: 11 pages, a major revision of gr-qc/0612061 and will be published in
the Chin. J. Phy
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