4,942 research outputs found
Towards gravitationally assisted negative refraction of light by vacuum
Propagation of electromagnetic plane waves in some directions in
gravitationally affected vacuum over limited ranges of spacetime can be such
that the phase velocity vector casts a negative projection on the time-averaged
Poynting vector. This conclusion suggests, inter alia, gravitationally assisted
negative refraction by vacuum.Comment: 6 page
Spin and Center of Mass in Axially Symmetric Einstein-Maxwell Spacetimes
We give a definition and derive the equations of motion for the center of
mass and angular momentum of an axially symmetric, isolated system that emits
gravitational and electromagnetic radiation. A central feature of this
formulation is the use of Newman-Unti cuts at null infinity that are generated
by worldlines of the spacetime. We analyze some consequences of the results and
comment on the generalization of this work to general asymptotically flat
spacetimes.Comment: 20 page
Can one detect a non-smooth null infinity?
It is shown that the precession of a gyroscope can be used to elucidate the
nature of the smoothness of the null infinity of an asymptotically flat
spacetime (describing an isolated body). A model for which the effects of
precession in the non-smooth null infinity case are of order is
proposed. By contrast, in the smooth version the effects are of order .
This difference should provide an effective criterion to decide on the nature
of the smoothness of null infinity.Comment: 6 pages, to appear in Class. Quantum Gra
Freely falling 2-surfaces and the quasi-local energy
We derive an expression for effective gravitational mass for any closed
spacelike 2-surface. This effective gravitational energy is defined directly
through the geometrical quantity of the freely falling 2-surface and thus is
well adapted to intuitive expectation that the gravitational mass should be
determined by the motion of test body moving freely in gravitational field. We
find that this effective gravitational mass has reasonable positive value for a
small sphere in the non-vacuum space-times and can be negative for vacuum case.
Further, this effective gravitational energy is compared with the quasi-local
energy based on the formalism of the General Relativity. Although some
gauge freedoms exist, analytic expressions of the quasi-local energy for vacuum
cases are same as the effective gravitational mass. Especially, we see that the
contribution from the cosmological constant is the same in general cases.Comment: 11 pages, no figures, REVTeX. Estimation of the effective mass of
small spheres in non-vaccum spacetime and Schwarzschild spacetime are added.
The negativity of the latter is discusse
Fast Scramblers Of Small Size
We investigate various geometrical aspects of the notion of `optical depth'
in the thermal atmosphere of black hole horizons. Optical depth has been
proposed as a measure of fast-crambling times in such black hole systems, and
the associated optical metric suggests that classical chaos plays a leading
role in the actual scrambling mechanism. We study the behavior of the optical
depth with the size of the system and find that AdS/CFT phase transitions with
topology change occur naturally as the scrambler becomes smaller than its
thermal length. In the context of detailed AdS/CFT models based on D-branes,
T-duality implies that small scramblers are described in terms of matrix
quantum mechanics.Comment: 14 pages, 3 figures. Added reference
Relativistic conservation laws and integral constraints for large cosmological perturbations
For every mapping of a perturbed spacetime onto a background and with any
vector field we construct a conserved covariant vector density ,
which is the divergence of a covariant antisymmetric tensor density, a
"superpotential". is linear in the energy-momentum tensor
perturbations of matter, which may be large; does not contain the
second order derivatives of the perturbed metric. The superpotential is
identically zero when perturbations are absent.
By integrating conserved vectors over a part \Si of a hypersurface of
the background, which spans a two-surface \di\Si, we obtain integral
relations between, on the one hand, initial data of the perturbed metric
components and the energy-momentum perturbations on \Si and, on the other
hand, the boundary values on \di\Si. We show that there are as many such
integral relations as there are different mappings, 's, \Si's and
\di\Si's. For given boundary values on \di\Si, the integral relations may
be interpreted as integral constraints (e.g., those of Traschen) on local
initial data including the energy-momentum perturbations. Conservation laws
expressed in terms of Killing fields \Bar\xi of the background become
"physical" conservation laws.
In cosmology, to each mapping of the time axis of a Robertson-Walker space on
a de Sitter space with the same spatial topology there correspond ten
conservation laws. The conformal mapping leads to a straightforward
generalization of conservation laws in flat spacetimes. Other mappings are also
considered. ...Comment: This paper, published 7 years ago, was found useful by some
researchers but originally was not put on the gr-qc website. Now it has been
retyped with very minor changes: few wordings have been modified and several
misprints occurring in the printed version correcte
Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
The article reviews the current status of a theoretical approach to the
problem of the emission of gravitational waves by isolated systems in the
context of general relativity. Part A of the article deals with general
post-Newtonian sources. The exterior field of the source is investigated by
means of a combination of analytic post-Minkowskian and multipolar
approximations. The physical observables in the far-zone of the source are
described by a specific set of radiative multipole moments. By matching the
exterior solution to the metric of the post-Newtonian source in the near-zone
we obtain the explicit expressions of the source multipole moments. The
relationships between the radiative and source moments involve many non-linear
multipole interactions, among them those associated with the tails (and
tails-of-tails) of gravitational waves. Part B of the article is devoted to the
application to compact binary systems. We present the equations of binary
motion, and the associated Lagrangian and Hamiltonian, at the third
post-Newtonian (3PN) order beyond the Newtonian acceleration. The
gravitational-wave energy flux, taking consistently into account the
relativistic corrections in the binary moments as well as the various tail
effects, is derived through 3.5PN order with respect to the quadrupole
formalism. The binary's orbital phase, whose prior knowledge is crucial for
searching and analyzing the signals from inspiralling compact binaries, is
deduced from an energy balance argument.Comment: 109 pages, 1 figure; this version is an update of the Living Review
article originally published in 2002; available on-line at
http://www.livingreviews.org
Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence
We describe the null geometry of a multiple black hole event horizon in terms
of a conformal rescaling of a flat space null hypersurface. For the prolate
spheroidal case, we show that the method reproduces the pair-of-pants shaped
horizon found in the numerical simulation of the head-on-collision of black
holes. For the oblate case, it reproduces the initially toroidal event horizon
found in the numerical simulation of collapse of a rotating cluster. The
analytic nature of the approach makes further conclusions possible, such as a
bearing on the hoop conjecture. From a time reversed point of view, the
approach yields a description of the past event horizon of a fissioning white
hole, which can be used as null data for the characteristic evolution of the
exterior space-time.Comment: 21 pages, 6 figures, revtex, to appear in Phys. Rev.
Gravitational radiation from compact binary systems: gravitational waveforms and energy loss to second post-Newtonian order
We derive the gravitational waveform and gravitational-wave energy flux
generated by a binary star system of compact objects (neutron stars or black
holes), accurate through second post-Newtonian order () beyond the lowest-order quadrupole approximation. We cast the
Einstein equations into the form of a flat-spacetime wave equation together
with a harmonic gauge condition, and solve it formally as a retarded integral
over the past null cone of the chosen field point. The part of this integral
that involves the matter sources and the near-zone gravitational field is
evaluated in terms of multipole moments using standard techniques; the
remainder of the retarded integral, extending over the radiation zone, is
evaluated in a novel way. The result is a manifestly convergent and finite
procedure for calculating gravitational radiation to arbitrary orders in a
post-Newtonian expansion. Through second post-Newtonian order, the radiation is
also shown to propagate toward the observer along true null rays of the
asymptotically Schwarzschild spacetime, despite having been derived using flat
spacetime wave equations. The method cures defects that plagued previous
``brute- force'' slow-motion approaches to the generation of gravitational
radiation, and yields results that agree perfectly with those recently obtained
by a mixed post-Minkowskian post-Newtonian method. We display explicit formulae
for the gravitational waveform and the energy flux for two-body systems, both
in arbitrary orbits and in circular orbits. In an appendix, we extend the
formalism to bodies with finite spatial extent, and derive the spin corrections
to the waveform and energy loss.Comment: 59 pages ReVTeX; Physical Review D, in press; figures available on
request to [email protected]
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