105 research outputs found
Metric of a tidally distorted, nonrotating black hole
The metric of a tidally distorted, nonrotating black hole is presented in a
light-cone coordinate system that penetrates the event horizon and possesses a
clear geometrical meaning. The metric is expressed as an expansion in powers of
r/R << 1, where r is a measure of distance from the black hole and R is the
local radius of curvature of the external spacetime; this is assumed to be much
larger than M, the mass of the black hole. The metric is calculated up to a
remainder of order (r/R)^4, and it depends on a family of tidal gravitational
fields which characterize the hole's local environment. The coordinate system
allows an easy identification of the event horizon, and expressions are derived
for its surface gravity and the rates at which the tidal interaction transfers
mass and angular momentum to the black hole.Comment: 4 pages. Final version, as it will appear in Physical Review Letter
Construction of the second-order gravitational perturbations produced by a compact object
Accurate calculation of the gradual inspiral motion in an extreme mass-ratio
binary system, in which a compact-object inspirals towards a supermassive
black-hole requires calculation of the interaction between the compact-object
and the gravitational perturbations that it induces. These metric perturbations
satisfy linear partial differential equations on a curved background spacetime
induced by the supermassive black-hole. At the point particle limit the
second-order perturbations equations have source terms that diverge as
, where is the distance from the particle. This singular behavior
renders the standard retarded solutions of these equations ill-defined. Here we
resolve this problem and construct well-defined and physically meaningful
solutions to these equations. We recently presented an outline of this
resolution [E. Rosenthal, Phys. Rev. D 72, 121503 (2005)]. Here we provide the
full details of this analysis. These second-order solutions are important for
practical calculations: the planned gravitational-wave detector LISA requires
preparation of waveform templates for the expected gravitational-waves.
Construction of templates with desired accuracy for extreme mass-ratio binaries
requires accurate calculation of the inspiral motion including the interaction
with the second-order gravitational perturbations.Comment: 30 page
Colliding axisymmetric pp-waves
An exact solution is found describing the collision of axisymmetric pp-waves
with M=0. They are impulsive in character and their coordinate singularities
become point curvature singularities at the boundaries of the interaction
region. The solution is conformally flat. Concrete examples are given,
involving an ultrarelativistic black hole against a burst of pure radiation or
two colliding beam- like waves.Comment: 6 pages, REVTeX, some misprints are correcte
Regularization of the second-order gravitational perturbations produced by a compact object
The equations for the second-order gravitational perturbations produced by a
compact-object have highly singular source terms at the point particle limit.
At this limit the standard retarded solutions to these equations are
ill-defined. Here we construct well-defined and physically meaningful solutions
to these equations. These solutions are important for practical calculations:
the planned gravitational-wave detector LISA requires preparation of waveform
templates for the potential gravitational-waves. Construction of templates with
desired accuracy for extreme mass ratio binaries, in which a compact-object
inspirals towards a supermassive black-hole, requires calculation of the
second-order gravitational perturbations produced by the compact-object.Comment: 12 pages, discussion expanded, to be published in Phys. Rev. D Rapid
Communicatio
Improved analysis of black hole formation in high-energy particle collisions
We investigate formation of an apparent horizon (AH) in high-energy particle
collisions in four- and higher-dimensional general relativity, motivated by
TeV-scale gravity scenarios. The goal is to estimate the prefactor in the
geometric cross section formula for the black hole production. We numerically
construct AHs on the future light cone of the collision plane. Since this slice
lies to the future of the slice used previously by Eardley and Giddings
(gr-qc/0201034) and by one of us and Nambu (gr-qc/0209003), we are able to
improve the prefactor estimates. The black hole production cross section
increases by 40-70% in the higher-dimensional cases, indicating larger black
hole production rates in future-planned accelerators than previously estimated.
We also determine the mass and the angular momentum of the final black hole
state, as allowed by the area theorem.Comment: 28 pages, 14 figures, references and minor comments adde
An approximate binary-black-hole metric
An approximate solution to Einstein's equations representing two
widely-separated non-rotating black holes in a circular orbit is constructed by
matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The
spacetime metric is presented in a single coordinate system valid up to the
apparent horizons of the black holes. This metric could be useful in numerical
simulations of binary black holes. Initial data extracted from this metric have
the advantages of being linked to the early inspiral phase of the binary
system, and of not containing spurious gravitational waves.Comment: 20 pages, 1 figure; some changes in Sec. IV B,C and Sec.
Close-limit analysis for head-on collision of two black holes in higher dimensions: Brill-Lindquist initial data
Motivated by the TeV-scale gravity scenarios, we study gravitational
radiation in the head-on collision of two black holes in higher dimensional
spacetimes using a close-limit approximation. We prepare time-symmetric initial
data sets for two black holes (the so-called Brill-Lindquist initial data) and
numerically evolve the spacetime in terms of a gauge invariant formulation for
the perturbation around the higher-dimensional Schwarzschild black holes. The
waveform and radiated energy of gravitational waves emitted in the head-on
collision are clarified. Also, the complex frequencies of fundamental
quasinormal modes of higher-dimensional Schwarzschild black holes, which have
not been accurately derived so far, are determined.Comment: 27 pages, 8 figures, published versio
On leading order gravitational backreactions in de Sitter spacetime
Backreactions are considered in a de Sitter spacetime whose cosmological
constant is generated by the potential of scalar field. The leading order
gravitational effect of nonlinear matter fluctuations is analyzed and it is
found that the initial value problem for the perturbed Einstein equations
possesses linearization instabilities. We show that these linearization
instabilities can be avoided by assuming strict de Sitter invariance of the
quantum states of the linearized fluctuations. We furthermore show that quantum
anomalies do not block the invariance requirement. This invariance constraint
applies to the entire spectrum of states, from the vacuum to the excited states
(should they exist), and is in that sense much stronger than the usual Poincare
invariance requirement of the Minkowski vacuum alone. Thus to leading order in
their effect on the gravitational field, the quantum states of the matter and
metric fluctuations must be de Sitter invariant.Comment: 12 pages, no figures, typos corrected and some clarifying comments
added, version accepted by Phys. Rev.
Gravitational Radiation from the radial infall of highly relativistic point particles into Kerr black holes
In this paper, we consider the gravitational radiation generated by the
collision of highly relativistic particles with rotating Kerr black holes. We
use the Sasaki-Nakamura formalism to compute the waveform, energy spectra and
total energy radiated during this process. We show that the gravitational
spectrum for high-energy collisions has definite characteristic universal
features, which are independent of the spin of the colliding objects. We also
discuss possible connections between these results and the black hole-black
hole collision at the speed of light process. With these results at hand, we
predict that during the high speed collision of a non-rotating hole with a
rotating one, about 35% of the total energy can get converted into
gravitational waves. Thus, if one is able to produce black holes at the Large
Hadron Collider, as much as 35% of the partons' energy should be emitted during
the so called balding phase. This energy will be missing, since we don't have
gravitational wave detectors able to measure such amplitudes. The collision at
the speed of light between one rotating black hole and a non-rotating one or
two rotating black holes turns out to be the most efficient gravitational wave
generator in the Universe.Comment: 15 pages, REVTEX4. Some comments and references adde
Second-order gravitational self-force
We derive an expression for the second-order gravitational self-force that
acts on a self-gravitating compact-object moving in a curved background
spacetime. First we develop a new method of derivation and apply it to the
derivation of the first-order gravitational self-force. Here we find that our
result conforms with the previously derived expression. Next we generalize our
method and derive a new expression for the second-order gravitational
self-force. This study also has a practical motivation: The data analysis for
the planned gravitational wave detector LISA requires construction of waveforms
templates for the expected gravitational waves. Calculation of the two leading
orders of the gravitational self-force will enable one to construct highly
accurate waveform templates, which are needed for the data analysis of
gravitational-waves that are emitted from extreme mass-ratio binaries.Comment: 35 page
- …