44 research outputs found
Gravitational Wave Emission and Mass Extraction from a Perturbed Schwarzschild Black Hole (continue)
A relativistic model for the emission of gravitational waves from an
initially unperturbed Schwarzschild black hole, or spherical collapsing
configuration, is completely integrated. The model consists basically of
gravitational perturbations of the Robinson-Trautman type on the Schwarzschild
spacetime. In our scheme of perturbation, gravitational waves may extract mass
from the collapsing configuration. Robinson-Trautmann perturbations also
include another mode of emission of mass, which we denote shell emission mode:
in the equatorial plane of the configuration, a timelike shell of
matter may be present, whose stress-energy tensor is modelled by neutrinos and
strings emitted radially on the shell; no gravitational waves are present in
this mode. The invariant characterization of gravitational wave perturbations
and of the gravitational wave zone is made through the analysis of the
structure of the curvature tensor and the use of the Peeling Theorem.Comment: 26 pages, LaTex, no figure
Gravitational wave recoils in non-axisymmetric Robinson-Trautman spacetimes
We examine the gravitational wave recoil waves and the associated net kick
velocities in non-axisymmetric Robinson-Trautman spacetimes. We use
characteristic initial data for the dynamics corresponding to non-head-on
collisions of black holes. We make a parameter study of the kick distributions,
corresponding to an extended range of the incidence angle in the
initial data. For the range of examined () the kick distributions as a function of the symmetric mass
parameter satisfy a law obtained from an empirical modification of the
Fitchett law, with a parameter that accounts for the non-zero net
gravitational momentum wave fluxes for the equal mass case. The law fits
accurately the kick distributions for the range of examined, with a
rms normalized error of the order of . For the equal mass case the
nonzero net gravitational wave momentum flux increases as increases,
up to beyond which it decreases. The maximum net
kick velocity is about for for the boost parameter considered.
For the distribution is a monotonous function of
. The angular patterns of the gravitational waves emitted are examined.
Our analysis includes the two polarization modes present in wave zone
curvature.Comment: 10 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1403.4581, arXiv:1202.1271, arXiv:1111.122
Chaos and a Resonance Mechanism for Structure Formation in Inflationary Models
We exhibit a resonance mechanism of amplification of density perturbations in
inflationary mo-dels, using a minimal set of ingredients (an effective
cosmological constant, a scalar field minimally coupled to the gravitational
field and matter), common to most models in the literature of inflation. This
mechanism is based on the structure of homoclinic cylinders, emanating from an
unstable periodic orbit in the neighborhood of a saddle-center critical point,
present in the phase space of the model. The cylindrical structure induces
oscillatory motions of the scales of the universe whenever the orbit visits the
neighborhood of the saddle-center, before the universe enters a period of
exponential expansion. The oscillations of the scale functions produce, by a
resonance mechanism, the amplification of a selected wave number spectrum of
density perturbations, and can explain the hierarchy of scales observed in the
actual universe. The transversal crossings of the homoclinic cylinders induce
chaos in the dynamics of the model, a fact intimately connected to the
resonance mechanism occuring immediately before the exit to inflation.Comment: 4 pages. This essay received an Honorable Mention from the Gravity
Research Foundation, 1998-Ed. To appear in Mod. Phys. Lett.
The low dimensional dynamical system approach in General Relativity: an example
In this paper we explore one of the most important features of the Galerkin
method, which is to achieve high accuracy with a relatively modest
computational effort, in the dynamics of Robinson-Trautman spacetimes.Comment: 7 pages, 5 figure
Galerkin Method in the Gravitational Collapse: a Dynamical System Approach
We study the general dynamics of the spherically symmetric gravitational
collapse of a massless scalar field. We apply the Galerkin projection method to
transform a system of partial differential equations into a set of ordinary
differential equations for modal coefficients, after a convenient truncation
procedure, largely applied to problems of turbulence. In the present case, we
have generated a finite dynamical system that reproduces the essential features
of the dynamics of the gravitational collapse, even for a lower order of
truncation. Each initial condition in the space of modal coefficients
corresponds to a well definite spatial distribution of scalar field. Numerical
experiments with the dynamical system show that depending on the strength of
the scalar field packet, the formation of black-holes or the dispersion of the
scalar field leaving behind flat spacetime are the two main outcomes. We also
found numerical evidence that between both asymptotic states, there is a
critical solution represented by a limit cycle in the modal space with period
.Comment: 9 pages, revtex4, 10 ps figures; Phys. Rev. D, in pres
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
Chaos in Anisotropic Pre-Inflationary Universes
We study the dynamics of anisotropic Bianchi type-IX models with matter and
cosmological constant. The models can be thought as describing the role of
anisotropy in the early stages of inflation. The concurrence of the
cosmological constant and anisotropy are sufficient to produce a chaotic
dynamics in the gravitational degrees of freedom, connected to the presence of
a critical point of saddle-center type in the phase space of the system. The
invariant character of chaos is guaranteed by the topology of the cylinders
emanating from unstable periodic orbits in the neighborhood of the
saddle-center. We discuss a possible mechanism for amplification of specific
wavelengths of inhomogeneous fluctuations in the models. A geometrical
interpretation is given for Wald's inequality in terms of invariant tori and
their destruction by increasing values of the cosmological constant.Comment: 14 pages, figures available under request. submitted to Physical
Review