227 research outputs found
Energy Distribution associated with Static Axisymmetric Solutions
This paper has been addressed to a very old but burning problem of energy in
General Relativity. We evaluate energy and momentum densities for the static
and axisymmetric solutions. This specializes to two metrics, i.e., Erez-Rosen
and the gamma metrics, belonging to the Weyl class. We apply four well-known
prescriptions of Einstein, Landau-Lifshitz, Papaterou and Mller to
compute energy-momentum density components. We obtain that these prescriptions
do not provide similar energy density, however momentum becomes constant in
each case. The results can be matched under particular boundary conditions.Comment: 18 pages, accepted for publication in Astrophysics and SpaceScienc
Gravitational Charged Perfect Fluid Collapse in Friedmann Universe Models
This paper is devoted to study the gravitational charged perfect fluid
collapse in the Friedmann universe models with cosmological constant. For this
purpose, we assume that the electromagnetic field is so weak that it does not
introduce any distortion into the geometry of the spacetime. The results
obtained from the junction conditions between the Friedmann and the
Reissner-Nordstrm de-Sitter spacetimes are used to solve the field
equations. Further, the singularity structure and mass effects of the
collapsing system on time difference between the formation of apparent horizons
and singularity have been studied. This analysis provides the validity of
Cosmic Censorship Hypothesis. It is found that the electric field affects the
area of apparent horizons and their time of formation.Comment: 17 pages, accepted for publication in Astrophys. Space Sc
Energy Distribution in f(R) Gravity
The well-known energy problem is discussed in f(R) theory of gravity. We use
the generalized Landau-Lifshitz energy-momentum complex in the framework of
metric f(R) gravity to evaluate the energy density of plane symmetric solutions
for some general f(R) models. In particular, this quantity is found for some
popular choices of f(R) models. The constant scalar curvature condition and the
stability condition for these models are also discussed. Further, we
investigate the energy distribution of cosmic string spacetime.Comment: 15 pages, accepted for publication in Gen. Relativ. & Gra
Newtonian Analysis of Gravitational Waves from Naked Singularity
Spherical dust collapse generally forms a shell focusing naked singularity at
the symmetric center. This naked singularity is massless. Further the Newtonian
gravitational potential and speed of the dust fluid elements are everywhere
much smaller than unity until the central shell focusing naked singularity
formation if an appropriate initial condition is set up. Although such a
situation is highly relativistic, the analysis by the Newtonian approximation
scheme is available even in the vicinity of the space-time singularity. This
remarkable feature makes the analysis of such singularity formation very easy.
We investigate non-spherical even-parity matter perturbations in this scheme by
complementary using numerical and semi-analytical approaches, and estimate
linear gravitational waves generated in the neighborhood of the naked
singularity by the quadrupole formula. The result shows good agreement with the
relativistic perturbation analysis recently performed by Iguchi et al. The
energy flux of the gravitational waves is finite but the space-time curvature
carried by them diverges.Comment: 23 pages, 8 figure
Gauge fixing and the Hamiltonian for cylindrical spacetimes
We introduce a complete gauge fixing for cylindrical spacetimes in vacuo
that, in principle, do not contain the axis of symmetry. By cylindrically
symmetric we understand spacetimes that possess two commuting spacelike Killing
vectors, one of them rotational and the other one translational. The result of
our gauge fixing is a constraint-free model whose phase space has four
field-like degrees of freedom and that depends on three constant parameters.
Two of these constants determine the global angular momentum and the linear
momentum in the axis direction, while the third parameter is related with the
behavior of the metric around the axis. We derive the explicit expression of
the metric in terms of the physical degrees of freedom, calculate the reduced
equations of motion and obtain the Hamiltonian that generates the reduced
dynamics. We also find upper and lower bounds for this reduced Hamiltonian that
provides the energy per unit length contained in the system. In addition, we
show that the reduced formalism constructed is well defined and consistent at
least when the linear momentum in the axis direction vanishes. Furthermore, in
that case we prove that there exists an infinite number of solutions in which
all physical fields are constant both in the surroundings of the axis and at
sufficiently large distances from it. If the global angular momentum is
different from zero, the isometry group of these solutions is generally not
orthogonally transitive. Such solutions generalize the metric of a spinning
cosmic string in the region where no closed timelike curves are present.Comment: 12 pages, accepted for publication in Physical Review
High-Speed Cylindrical Collapse of Two Perfect Fluids
In this paper, the study of the gravitational collapse of cylindrically
distributed two perfect fluid system has been carried out. It is assumed that
the collapsing speeds of the two fluids are very large. We explore this
condition by using the high-speed approximation scheme. There arise two cases,
i.e., bounded and vanishing of the ratios of the pressures with densities of
two fluids given by . It is shown that the high-speed approximation
scheme breaks down by non-zero pressures when are bounded
below by some positive constants. The failure of the high-speed approximation
scheme at some particular time of the gravitational collapse suggests the
uncertainity on the evolution at and after this time. In the bounded case, the
naked singularity formation seems to be impossible for the cylindrical two
perfect fluids. For the vanishing case, if a linear equation of state is used,
the high-speed collapse does not break down by the effects of the pressures and
consequently a naked singularity forms. This work provides the generalisation
of the results already given by Nakao and Morisawa [1] for the perfect fluid.Comment: 11 pages, 1 figure, accepted for publication in Gen. Rel. Gra
Minimum black hole mass from colliding Gaussian packets
We study the formation of a black hole in the collision of two Gaussian
packets. Rather than following their dynamical evolution in details, we assume
a horizon forms when the mass function for the two packets becomes larger than
half the flat areal radius, as it would occur in a spherically symmetric
geometry. This simple approximation allows us to determine the existence of a
minimum black hole mass solely related to the width of the packets. We then
comment on the possible physical implications, both in classical and quantum
physics, and models with extra spatial dimensions.Comment: 11 pages, 4 figure
Energy Distribution for Non-commutative Radiating Schwarzschild Black Holes
The aim of this article is the calculation of the energy-momentum for a
non-commutative radiating Schwarzschild black hole in order to obtain the
expressions for energy. We make the calculations with the Einstein and M\oller
prescriptions. We show that the expressions for energy in both the
prescriptions depend on the mass , parameter and radial coordinate.
We make some comparisons between the results. Our results show that the
Einstein prescription is a more powerful concept than the M\oller prescription.Comment: 5 pages and 6 figures. Revised version submitted in Int.J.Theor.Phys.
after minor revisio
Ten Proofs of the Generalized Second Law
Ten attempts to prove the Generalized Second Law of Thermodyanmics (GSL) are
described and critiqued. Each proof provides valuable insights which should be
useful for constructing future, more complete proofs. Rather than merely
summarizing previous research, this review offers new perspectives, and
strategies for overcoming limitations of the existing proofs. A long
introductory section addresses some choices that must be made in any
formulation the GSL: Should one use the Gibbs or the Boltzmann entropy? Should
one use the global or the apparent horizon? Is it necessary to assume any
entropy bounds? If the area has quantum fluctuations, should the GSL apply to
the average area? The definition and implications of the classical,
hydrodynamic, semiclassical and full quantum gravity regimes are also
discussed. A lack of agreement regarding how to define the "quasi-stationary"
regime is addressed by distinguishing it from the "quasi-steady" regime.Comment: 60 pages, 2 figures, 1 table. v2: corrected typos and added a
footnote to match the published versio
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