137 research outputs found
Mode-coupling in rotating gravitational collapse: Gravitational and electromagnetic perturbations
We consider the late-time evolution of {\it gravitational} and
electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We
give a detailed analysis of the mode-coupling phenomena in rotating
gravitational collapse. A consequence of this phenomena is that the late-time
tail is dominated by modes which, in general, may have an angular distribution
different from the original one. In addition, we show that different types of
fields have {\it different} decaying rates. This result turns over the
traditional belief (which has been widely accepted during the last three
decades) that the late-time tail of gravitational collapse is universal.Comment: 16 page
Radiation tails and boundary conditions for black hole evolutions
In numerical computations of Einstein's equations for black hole spacetimes,
it will be necessary to use approximate boundary conditions at a finite
distance from the holes. We point out here that ``tails,'' the inverse
power-law decrease of late-time fields, cannot be expected for such
computations. We present computational demonstrations and discussions of
features of late-time behavior in an evolution with a boundary condition.Comment: submitted to Phys. Rev.
Radiative falloff in Schwarzschild-de Sitter spacetime
We consider the time evolution of a scalar field propagating in
Schwarzschild-de Sitter spacetime. At early times, the field behaves as if it
were in pure Schwarzschild spacetime; the structure of spacetime far from the
black hole has no influence on the evolution. In this early epoch, the field's
initial outburst is followed by quasi-normal oscillations, and then by an
inverse power-law decay. At intermediate times, the power-law behavior gives
way to a faster, exponential decay. At late times, the field behaves as if it
were in pure de Sitter spacetime; the structure of spacetime near the black
hole no longer influences the evolution in a significant way. In this late
epoch, the field's behavior depends on the value of the curvature-coupling
constant xi. If xi is less than a critical value 3/16, the field decays
exponentially, with a decay constant that increases with increasing xi. If xi >
3/16, the field oscillates with a frequency that increases with increasing xi;
the amplitude of the field still decays exponentially, but the decay constant
is independent of xi.Comment: 10 pages, ReVTeX, 5 figures, references updated, and new section
adde
The motion of point particles in curved spacetime
This review is concerned with the motion of a point scalar charge, a point
electric charge, and a point mass in a specified background spacetime. In each
of the three cases the particle produces a field that behaves as outgoing
radiation in the wave zone, and therefore removes energy from the particle. In
the near zone the field acts on the particle and gives rise to a self-force
that prevents the particle from moving on a geodesic of the background
spacetime. The field's action on the particle is difficult to calculate because
of its singular nature: the field diverges at the position of the particle. But
it is possible to isolate the field's singular part and show that it exerts no
force on the particle -- its only effect is to contribute to the particle's
inertia. What remains after subtraction is a smooth field that is fully
responsible for the self-force. Because this field satisfies a homogeneous wave
equation, it can be thought of as a free (radiative) field that interacts with
the particle; it is this interaction that gives rise to the self-force. The
mathematical tools required to derive the equations of motion of a point scalar
charge, a point electric charge, and a point mass in a specified background
spacetime are developed here from scratch. The review begins with a discussion
of the basic theory of bitensors (part I). It then applies the theory to the
construction of convenient coordinate systems to chart a neighbourhood of the
particle's word line (part II). It continues with a thorough discussion of
Green's functions in curved spacetime (part III). The review concludes with a
detailed derivation of each of the three equations of motion (part IV).Comment: LaTeX2e, 116 pages, 10 figures. This is the final version, as it will
appear in Living Reviews in Relativit
Self force on static charges in Schwarzschild spacetime
We study the self forces acting on static scalar and electric test charges in
the spacetime of a Schwarzschild black hole. The analysis is based on a direct,
local calculation of the self forces via mode decomposition, and on two
independent regularization procedures: A spatially-extended particle model
method, and on a mode-sum regularization prescription. In all cases we find
excellent agreement with the known exact results.Comment: 21 pages, 9 Encapsulated PostScript figures, submitted to Class.
Quantum Gra
High-Order Contamination in the Tail of Gravitational Collapse
It is well known that the late-time behaviour of gravitational collapse is
{\it dominated} by an inverse power-law decaying tail. We calculate {\it
higher-order corrections} to this power-law behaviour in a spherically
symmetric gravitational collapse. The dominant ``contamination'' is shown to
die off at late times as . This decay rate is much {\it
slower} than has been considered so far. It implies, for instance, that an
`exact' (numerical) determination of the power index to within
requires extremely long integration times of order . We show that the
leading order fingerprint of the black-hole electric {\it charge} is of order
.Comment: 12 pages, 2 figure
Black hole collision with a scalar particle in three dimensional anti-de Sitter spacetime
We study the collision between a BTZ black hole and a test particle coupled
to a scalar field. We compute the power spectrum, the energy radiated and the
plunging waveforms for this process. We show that for late times the signal is
dominated by the quasinormal ringing. In terms of the AdS/CFT correspondence
the bulk gravity process maps into a thermal state, an expanding bubble and
gauge particles decaying into bosons of the associated operator. These latter
thermalize in a timescale predicted by the bulk theory.Comment: 5 pages, 3 figures;minor improvements; references adde
Understanding the importance of transient resonances in extreme mass ratio inspirals
Extreme mass ratio inspirals (EMRIs) occur when a compact object orbits a
much larger one, like a solar-mass black hole around a supermassive black hole.
The orbit has 3 frequencies which evolve through the inspiral. If the orbital
radial frequency and polar frequency become commensurate, the system passes
through a transient resonance. Evolving through resonance causes a jump in the
evolution of the orbital parameters. We study these jumps and their impact on
EMRI gravitational-wave detection. Jumps are smaller for lower eccentricity
orbits; since most EMRIs have small eccentricities when passing through
resonances, we expect that the impact on detection will be small. Neglecting
the effects of transient resonances leads to a loss of ~4% of detectable
signals for an astrophysically motivated population of EMRIs.Comment: 2 pages, 0 figures; to appear in the proceedings of the 11th
International LISA Symposiu
Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits
Observations have established that extremely compact, massive objects are
common in the universe. It is generally accepted that these objects are black
holes. As observations improve, it becomes possible to test this hypothesis in
ever greater detail. In particular, it is or will be possible to measure the
properties of orbits deep in the strong field of a black hole candidate (using
x-ray timing or with gravitational-waves) and to test whether they have the
characteristics of black hole orbits in general relativity. Such measurements
can be used to map the spacetime of a massive compact object, testing whether
the object's multipoles satisfy the strict constraints of the black hole
hypothesis. Such a test requires that we compare against objects with the
``wrong'' multipole structure. In this paper, we present tools for constructing
bumpy black holes: objects that are almost black holes, but that have some
multipoles with the wrong value. The spacetimes which we present are good deep
into the strong field of the object -- we do not use a large r expansion,
except to make contact with weak field intuition. Also, our spacetimes reduce
to the black hole spacetimes of general relativity when the ``bumpiness'' is
set to zero. We propose bumpy black holes as the foundation for a null
experiment: if black hole candidates are the black holes of general relativity,
their bumpiness should be zero. By comparing orbits in a bumpy spacetime with
those of an astrophysical source, observations should be able to test this
hypothesis, stringently testing whether they are the black holes of general
relativity. (Abridged)Comment: 16 pages + 2 appendices + 3 figures. Submitted to PR
Intermediate and extreme mass-ratio inspirals — astrophysics, science applications and detection using LISA
Black hole binaries with extreme (gtrsim104:1) or intermediate (~102–104:1) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed laser interferometer space antenna (LISA). These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany
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