481 research outputs found
Gravitational lens optical scalars in terms of energy-momentum distributions
This is a general work on gravitational lensing. We present new expressions
for the optical scalars and the deflection angle in terms of the
energy-momentum tensor components of matter distributions. Our work generalizes
standard references in the literature where normally stringent assumptions are
made on the sources. The new expressions are manifestly gauge invariant, since
they are presented in terms of curvature components. We also present a method
of approximation for solving the lens equations, that can be applied to any
order.Comment: 17 pages, 2 figures. Titled changed. Small improvements. References
added. Final version published in Phys.Rev.
Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes
In [arXiv:0803.3259] the equations describing the parallel transport of
orthonormal frames along timelike (spacelike) geodesics in a spacetime
admitting a non-degenerate principal conformal Killing-Yano 2-form h were
solved. The construction employed is based on studying the Darboux subspaces of
the 2-form F obtained as a projection of h along the geodesic trajectory. In
this paper we demonstrate that, although slightly modified, a similar
construction is possible also in the case of null geodesics. In particular, we
explicitly construct the parallel-transported frames along null geodesics in
D=4,5,6 Kerr-NUT-(A)dS spacetimes. We further discuss the parallel transport
along principal null directions in these spacetimes. Such directions coincide
with the eigenvectors of the principal conformal Killing-Yano tensor. Finally,
we show how to obtain a parallel-transported frame along null geodesics in the
background of the 4D Plebanski-Demianski metric which admits only a conformal
generalization of the Killing-Yano tensor.Comment: 17 pages, no figure
On the Significance of the Weyl Curvature in a Relativistic Cosmological Model
The Weyl curvature includes the Newtonian field and an additional field, the
so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci
identities to provide a set of constraints and propagations for the Weyl
fields. The temporal evolutions of propagations manifest explicit solutions of
gravitational waves. We see that models with purely Newtonian field are
inconsistent with relativistic models and obstruct sounding solutions.
Therefore, both fields are necessary for the nonlocal nature and radiative
solutions of gravitation.Comment: 15 pages, incorporating proof correction
Gravitational Wave Propagation in Isotropic Cosmologies
We study the propagation of gravitational waves carrying arbitrary
information through isotropic cosmologies. The waves are modelled as small
perturbations of the background Robertson-Walker geometry. The perfect fluid
matter distribution of the isotropic background is, in general, modified by
small anisotropic stresses. For pure gravity waves, in which the perturbed Weyl
tensor is radiative (i.e. type N in the Petrov classification), we construct
explicit examples for which the presence of the anisotropic stress is shown to
be essential and the histories of the wave-fronts in the background
Robertson-Walker geometry are shear-free null hypersurfaces. The examples
derived in this case are analogous to the Bateman waves of electromagnetic
theory.Comment: 27 pages, accepted for publication in Phys.Rev.
Gravitational Wave Emission from a Bounded Source: the Nonlinear Regime
We study the dynamics of a bounded gravitational collapsing configuration
emitting gravitational waves, where the exterior spacetime is described by
Robinson-Trautman geometries. The full nonlinear regime is examined by using
the Galerkin method that allows us to reduce the equations governing the
dynamics to a finite-dimensional dynamical system, after a proper truncation
procedure. Amongst the obtained results of the nonlinear evolution, one of the
most impressive is the fact that the distribution of the mass fraction
extracted by gravitational wave emission satisfies the distribution law of
nonextensive statistics and this result is independent of the initial
configurations considered.Comment: 3 page, 1 figure, proceedings of the X Marcel Grossmann Meeting 22-26
July, 2003, Rio de Janeir
The Efficiency of Gravitational Bremsstrahlung Production in the Collision of Two Schwarzschild Black Holes
We examine the efficiency of gravitational bremsstrahlung production in the
process of head-on collision of two boosted Schwarzschild black holes. We
constructed initial data for the characteristic initial value problem in
Robinson-Trautman spacetimes, that represent two instantaneously stationary
Schwarzschild black holes in motion towards each other with the same velocity.
The Robinson-Trautman equation was integrated for these initial data using a
numerical code based on the Galerkin method. The final resulting configuration
is a boosted black hole with Bondi mass greater than the sum of the individual
mass of each initial black hole. Two relevant aspects of the process are
presented. The first relates the efficiency of the energy extraction
by gravitational wave emission to the mass of the final black hole. This
relation is fitted by a distribution function of non-extensive thermostatistics
with entropic parameter ; the result extends and validates
analysis based on the linearized theory of gravitational wave emission. The
second is a typical bremsstrahlung angular pattern in the early period of
emission at the wave zone, a consequence of the deceleration of the black holes
as they coalesce; this pattern evolves to a quadrupole form for later times.Comment: 16 pages, 4 figures, to appear in Int. J. Modern Phys. D (2008
Dotted and Undotted Algebraic Spinor Fields in General Relativity
We investigate using Clifford algebra methods the theory of algebraic dotted
and undotted spinor fields over a Lorentzian spacetime and their realizations
as matrix spinor fields, which are the usual dotted and undotted two component
spinor fields. We found that some ad hoc rules postulated for the covariant
derivatives of Pauli sigma matrices and also for the Dirac gamma matrices in
General Relativity cover important physical meaning, which is not apparent in
the usual matrix presentation of the theory of two components dotted and
undotted spinor fields. We also discuss some issues related to the the previous
one and which appear in a proposed "unified" theory of gravitation and
electromagnetism which use two components dotted and undotted spinor fields and
also paravector fields, which are particular sections of the even subundle of
the Clifford bundle of spacetime.Comment: some new misprints have been correcte
Dynamics of test bodies with spin in de Sitter spacetime
We study the motion of spinning test bodies in the de Sitter spacetime of
constant positive curvature. With the help of the 10 Killing vectors, we derive
the 4-momentum and the tensor of spin explicitly in terms of the spacetime
coordinates. However, in order to find the actual trajectories, one needs to
impose the so-called supplementary condition. We discuss the dynamics of
spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.Comment: 11 pages, RevTex forma
Gravitational Waves Astronomy: a cornerstone for gravitational theories
Realizing a gravitational wave (GW) astronomy in next years is a great
challenge for the scientific community. By giving a significant amount of new
information, GWs will be a cornerstone for a better understanding of
gravitational physics. In this paper we re-discuss that the GW astronomy will
permit to solve a captivating issue of gravitation. In fact, it will be the
definitive test for Einstein's general relativity (GR), or, alternatively, a
strong endorsement for extended theories of gravity (ETG).Comment: To appear in Proceedings of the Workshop "Cosmology, the Quantum
Vacuum and Zeta Functions" for the celebration of Emilio Elizalde's sixtieth
birthday, Barcelona, March 8-10, 201
On the propagation of jump discontinuities in relativistic cosmology
A recent dynamical formulation at derivative level \ptl^{3}g for fluid
spacetime geometries , that employs the concept
of evolution systems in first-order symmetric hyperbolic format, implies the
existence in the Weyl curvature branch of a set of timelike characteristic
3-surfaces associated with propagation speed |v| = \sfrac{1}{2} relative to
fluid-comoving observers. We show it is the physical role of the constraint
equations to prevent realisation of jump discontinuities in the derivatives of
the related initial data so that Weyl curvature modes propagating along these
3-surfaces cannot be activated. In addition we introduce a new, illustrative
first-order symmetric hyperbolic evolution system at derivative level
\ptl^{2}g for baryotropic perfect fluid cosmological models that are
invariant under the transformations of an Abelian isometry group.Comment: 19 pages, 1 table, REVTeX v3.1 (10pt), submitted for publication to
Physical Review D; added Report-No, corrected typo
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