128 research outputs found
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.
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.
Electromagnetic radiation from collisions at almost the speed of light: an extremely relativistic charged particle falling into a Schwarzschild black hole
We investigate the electromagnetic radiation released during the high energy
collision of a charged point particle with a four-dimensional Schwarzschild
black hole. We show that the spectra is flat, and well described by a classical
calculation. We also compare the total electromagnetic and gravitational
energies emitted, and find that the former is supressed in relation to the
latter for very high energies. These results could apply to the astrophysical
world in the case charged stars and small charged black holes are out there
colliding into large black holes, and to a very high energy collision
experiment in a four-dimensional world. In this latter scenario the calculation
is to be used for the moments just after the black hole formation, when the
collision of charged debris with the newly formed black hole is certainly
expected. Since the calculation is four-dimensional, it does not directly apply
to Tev-scale gravity black holes, as these inhabit a world of six to eleven
dimensions, although our results should qualitatively hold when extrapolated
with some care to higher dimensions.Comment: 6 pages, 2 figure
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
Radiation from a D-dimensional collision of shock waves: first order perturbation theory
We study the spacetime obtained by superimposing two equal Aichelburg-Sexl
shock waves in D dimensions traveling, head-on, in opposite directions.
Considering the collision in a boosted frame, one shock becomes stronger than
the other, and a perturbative framework to compute the metric in the future of
the collision is setup. The geometry is given, in first order perturbation
theory, as an integral solution, in terms of initial data on the null surface
where the strong shock has support. We then extract the radiation emitted in
the collision by using a D-dimensional generalisation of the Landau-Lifschitz
pseudo-tensor and compute the percentage of the initial centre of mass energy
epsilon emitted as gravitational waves. In D=4 we find epsilon=25.0%, in
agreement with the result of D'Eath and Payne. As D increases, this percentage
increases monotonically, reaching 40.0% in D=10. Our result is always within
the bound obtained from apparent horizons by Penrose, in D=4, yielding 29.3%,
and Eardley and Giddings, in D> 4, which also increases monotonically with
dimension, reaching 41.2% in D=10. We also present the wave forms and provide a
physical interpretation for the observed peaks, in terms of the null generators
of the shocks.Comment: 27 pages, 11 figures; v2 some corrections, including D dependent
factor in epsilon; matches version accepted in JHE
Metric of a tidally perturbed spinning black hole
We explicitly construct the metric of a Kerr black hole that is tidally
perturbed by the external universe in the slow-motion approximation. This
approximation assumes that the external universe changes slowly relative to the
rotation rate of the hole, thus allowing the parameterization of the
Newman-Penrose scalar by time-dependent electric and magnetic tidal
tensors. This approximation, however, does not constrain how big the spin of
the background hole can be and, in principle, the perturbed metric can model
rapidly spinning holes. We first generate a potential by acting with a
differential operator on . From this potential we arrive at the metric
perturbation by use of the Chrzanowski procedure in the ingoing radiation
gauge. We provide explicit analytic formulae for this metric perturbation in
spherical Kerr-Schild coordinates, where the perturbation is finite at the
horizon. This perturbation is parametrized by the mass and Kerr spin parameter
of the background hole together with the electric and magnetic tidal tensors
that describe the time evolution of the perturbation produced by the external
universe. In order to take the metric accurate far away from the hole, these
tidal tensors should be determined by asymptotically matching this metric to
another one valid far from the hole. The tidally perturbed metric constructed
here could be useful in initial data constructions to describe the metric near
the horizons of a binary system of spinning holes. This perturbed metric could
also be used to construct waveforms and study the absorption of mass and
angular momentum by a Kerr black hole when external processes generate
gravitational radiation.Comment: 17 pages, 3 figures. Final PRD version, minor typos, etc corrected.
v3: corrected typo in Eq. (35) and (57
Quantum Einstein-Dirac Bianchi Universes
We study the mini--superspace quantization of spatially homogeneous (Bianchi)
cosmological universes sourced by a Dirac spinor field. The quantization of the
homogeneous spinor leads to a finite-dimensional fermionic Hilbert space and
thereby to a multi-component Wheeler-DeWitt equation whose main features are:
(i) the presence of spin-dependent Morse-type potentials, and (ii) the
appearance of a q-number squared-mass term, which is of order , and which is affected by ordering ambiguities. We give the exact
quantum solution of the Bianchi type-II system (which contains both scattering
states and bound states), and discuss the main qualitative features of the
quantum dynamics of the (classically chaotic) Bianchi type-IX system. We
compare the exact quantum dynamics of fermionic cosmological billiards to
previous works that described the spinor field as being either classical or
Grassmann-valued.Comment: 50 page
Negative Energy, Superluminosity and Holography
The holographic connection between large Super Yang Mills theory and
gravity in anti deSitter space requires unfamiliar behavior of the SYM theory
in the limit that the curvature of the AdS geometry becomes small. The
paradoxical behavior includes superluminal oscillations and negative energy
density. These effects typically occur in the SYM description of events which
take place far from the boundary of AdS when the signal from the event arrives
at the boundary. The paradoxes can be resolved by assuming a very rich
collection of hidden degrees of freedom of the SYM theory which store
information but give rise to no local energy density. These degrees of freedom,
called precursors, are needed to make possible sudden apparently acausal energy
momentum flows. Such behavior would be impossible in classical field theory as
a consequence of the positivity of the energy density. However we show that
these effects are not only allowed in quantum field theory but that we can
model them in free quantum field theory.Comment: Expanded version replacing earlier hep-th/990218
Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries
Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with
eliminated spin supplementary condition) for the next-to-leading order
spin-squared dynamics of general compact binaries is presented. The Hamiltonian
is applicable to the spin dynamics of all kinds of binaries with
self-gravitating components like black holes and/or neutron stars taking into
account spin-induced quadrupolar deformation effects in second post-Newtonian
order perturbation theory of Einstein's field equations. The corresponding
equations of motion for spin, position and momentum variables are given in
terms of canonical Poisson brackets. Comparison with a nonreduced potential
calculated within the Effective Field Theory approach is made.Comment: 11 pages, minor changes to match published version at CQ
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
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