583 research outputs found
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
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
Hamiltonian of a spinning test-particle in curved spacetime
Using a Legendre transformation, we compute the unconstrained Hamiltonian of
a spinning test-particle in a curved spacetime at linear order in the particle
spin. The equations of motion of this unconstrained Hamiltonian coincide with
the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac
brackets to derive the constrained Hamiltonian and the corresponding
phase-space algebra in the Newton-Wigner spin supplementary condition (SSC),
suitably generalized to curved spacetime, and find that the phase-space algebra
(q,p,S) is canonical at linear order in the particle spin. We provide explicit
expressions for this Hamiltonian in a spherically symmetric spacetime, both in
isotropic and spherical coordinates, and in the Kerr spacetime in
Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when
expanded in Post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner
(ADM) canonical Hamiltonian computed in PN theory in the test-particle limit.
Notably, we recover the known spin-orbit couplings through 2.5PN order and the
spin-spin couplings of type S_Kerr S (and S_Kerr^2) through 3PN order, S_Kerr
being the spin of the Kerr spacetime. Our method allows one to compute the PN
Hamiltonian at any order, in the test-particle limit and at linear order in the
particle spin. As an application we compute it at 3.5PN order.Comment: Corrected typo in the ADM Hamiltonian at 3.5 PN order (eq. 6.20
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
Gravitons and Lightcone Fluctuations
Gravitons in a squeezed vacuum state, the natural result of quantum creation
in the early universe or by black holes, will introduce metric fluctuations.
These metric fluctuations will introduce fluctuations of the lightcone. It is
shown that when the various two-point functions of a quantized field are
averaged over the metric fluctuations, the lightcone singularity disappears for
distinct points. The metric averaged functions remain singular in the limit of
coincident points. The metric averaged retarded Green's function for a massless
field becomes a Gaussian which is nonzero both inside and outside of the
classical lightcone. This implies some photons propagate faster than the
classical light speed, whereas others propagate slower. The possible effects of
metric fluctuations upon one-loop quantum processes are discussed and
illustrated by the calculation of the one-loop electron self-energy.Comment: 18pp, LATEX, TUTP-94-1
Curvature invariants in type N spacetimes
Scalar curvature invariants are studied in type N solutions of vacuum
Einstein's equations with in general non-vanishing cosmological constant
Lambda. Zero-order invariants which include only the metric and Weyl (Riemann)
tensor either vanish, or are constants depending on Lambda. Even all
higher-order invariants containing covariant derivatives of the Weyl (Riemann)
tensor are shown to be trivial if a type N spacetime admits a non-expanding and
non-twisting null geodesic congruence.
However, in the case of expanding type N spacetimes we discover a
non-vanishing scalar invariant which is quartic in the second derivatives of
the Riemann tensor.
We use this invariant to demonstrate that both linearized and the third order
type N twisting solutions recently discussed in literature contain
singularities at large distances and thus cannot describe radiation fields
outside bounded sources.Comment: 17 pages, to appear in Class. Quantum Gra
Explicit Kundt type II and N solutions as gravitational waves in various type D and O universes
A particular yet large class of non-diverging solutions which admits a
cosmological constant, electromagnetic field, pure radiation and/or general
non-null matter component is explicitly presented. These spacetimes represent
exact gravitational waves of arbitrary profiles which propagate in background
universes such as Minkowski, conformally flat (anti-)de Sitter, Edgar-Ludwig,
Bertotti-Robinson, and type D (anti-)Nariai or Plebanski-Hacyan spaces, and
their generalizations. All possibilities are discussed and are interpreted
using a unifying simple metric form. Sandwich and impulsive waves propagating
in the above background spaces with different geometries and matter content can
easily be constructed. New solutions are identified, e.g. type D pure radiation
or explicit type II electrovacuum waves in (anti-)Nariai universe. It is also
shown that, in general, there are no conformally flat Einstein-Maxwell fields
with a non-vanishing cosmological constant.Comment: 17 pages, LaTeX 2e. v2: added two references concerning generalized
Kerr-Schild transformations, minor changes in the tex
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
A Characterisation of the Weylian Structure of Space-Time by Means of Low Velocity Tests
The compatibility axiom in Ehlers, Pirani and Schild's (EPS) constructive
axiomatics of the space-time geometry that uses light rays and freely falling
particles with high velocity, is replaced by several constructions with low
velocity particles only. For that purpose we describe in a space-time with a
conformal structure and an arbitrary path structure the radial acceleration, a
Coriolis acceleration and the zig-zag construction. Each of these quantities
give effects whose requirement to vanish can be taken as alternative version of
the compatibility axiom of EPS. The procedural advantage lies in the fact, that
one can make null-experiments and that one only needs low velocity particles to
test the compatibility axiom. We show in addition that Perlick's standard clock
can exist in a Weyl space only.Comment: to appear in Gen.Rel.Gra
Mathisson's helical motions for a spinning particle --- are they unphysical?
It has been asserted in the literature that Mathisson's helical motions are
unphysical, with the argument that their radius can be arbitrarily large. We
revisit Mathisson's helical motions of a free spinning particle, and observe
that such statement is unfounded. Their radius is finite and confined to the
disk of centroids. We argue that the helical motions are perfectly valid and
physically equivalent descriptions of the motion of a spinning body, the
difference between them being the choice of the representative point of the
particle, thus a gauge choice. We discuss the kinematical explanation of these
motions, and we dynamically interpret them through the concept of hidden
momentum. We also show that, contrary to previous claims, the frequency of the
helical motions coincides, even in the relativistic limit, with the
zitterbewegung frequency of the Dirac equation for the electron
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