11,552 research outputs found
General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry
The Hamiltonian formulation of general relativity on a null surface is
established in the teleparallel geometry. No particular gauge conditons on the
tetrads are imposed, such as the time gauge condition. By means of a 3+1
decomposition the resulting Hamiltonian arises as a completely constrained
system. However, it is structurally different from the the standard
Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the
basic field quantities are tetrads that transform under the global SO(3,1) and
the torsion tensor.Comment: 15 pages, Latex, no figures, to appear in the Gen. Rel. Gra
Techniques for the realization of ultrareliable spaceborne computers Interim scientific report
Error-free ultrareliable spaceborne computer
Reionization Revisited: Secondary CMB Anisotropies and Polarization
Secondary CMB anisotropies and polarization provide a laboratory to study
structure formation in the reionized epoch. We consider the kinetic
Sunyaev-Zel'dovich effect from mildly nonlinear large-scale structure and show
that it is a natural extension of the perturbative Vishniac effect. If the gas
traces the dark matter to overdensities of order 10, as expected from
simulations, this effect is at least comparable to the Vishniac effect at
arcminute scales. On smaller scales, it may be used to study the thermal
history-dependent clustering of the gas. Polarization is generated through
Thomson scattering of primordial quadrupole anisotropies, kinetic (second order
Doppler) quadrupole anisotropies and intrinsic scattering quadrupole
anisotropies. Small scale polarization results from the density and ionization
modulation of these sources. These effects generically produce comparable E and
B-parity polarization, but of negligible amplitude (0.001-0.01 uK) in adiabatic
CDM models. However, the primordial and kinetic quadrupoles are observationally
comparable today so that a null detection of B-polarization would set
constraints on the evolution and coherence of the velocity field. Conversely, a
detection of a cosmological B-polarization even at large angles does not
necessarily imply the presence of gravity waves or vorticity. For these
calculations, we develop an all-sky generalization of the Limber equation that
allows for an arbitrary local angular dependence of the source for both scalar
and symmetric trace-free tensor fields on the sky.Comment: 14 pages, 12 figures, minor changes and typo fixes reflect published
versio
Gravitational waves from binary systems in circular orbits: Convergence of a dressed multipole truncation
The gravitational radiation originating from a compact binary system in
circular orbit is usually expressed as an infinite sum over radiative multipole
moments. In a slow-motion approximation, each multipole moment is then
expressed as a post-Newtonian expansion in powers of v/c, the ratio of the
orbital velocity to the speed of light. The bare multipole truncation of the
radiation consists in keeping only the leading-order term in the post-Newtonian
expansion of each moment, but summing over all the multipole moments. In the
case of binary systems with small mass ratios, the bare multipole series was
shown in a previous paper to converge for all values v/c < 2/e, where e is the
base of natural logarithms. In this paper, we extend the analysis to a dressed
multipole truncation of the radiation, in which the leading-order moments are
corrected with terms of relative order (v/c)^2 and (v/c)^3. We find that the
dressed multipole series converges also for all values v/c < 2/e, and that it
coincides (within 1%) with the numerically ``exact'' results for v/c < 0.2.Comment: 9 pages, ReVTeX, 1 postscript figur
Geometry of weak lensing of CMB polarization
Hu [Phys. Rev. D62 (2000) 043007] has presented a harmonic-space method for
calculating the effects of weak gravitational lensing on the cosmic microwave
background (CMB) over the full sky. Computing the lensed power spectra to first
order in the deflection power requires one to formulate the lensing
displacement beyond the tangent-space approximation. We point out that for CMB
polarization this displacement must undergo geometric corrections on the
spherical sky to maintain statistical isotropy of the lensed fields. Although
not discussed by Hu, these geometric effects are implicit in his analysis.
However, there they are hidden by an overly-compact notation that is both
unconventional and rather confusing. Here we aim to ameliorate this deficiency
by providing a rigorous derivation of the lensed spherical power spectra.Comment: 3 page
Design of a fault tolerant airborne digital computer. Volume 1: Architecture
This volume is concerned with the architecture of a fault tolerant digital computer for an advanced commercial aircraft. All of the computations of the aircraft, including those presently carried out by analogue techniques, are to be carried out in this digital computer. Among the important qualities of the computer are the following: (1) The capacity is to be matched to the aircraft environment. (2) The reliability is to be selectively matched to the criticality and deadline requirements of each of the computations. (3) The system is to be readily expandable. contractible, and (4) The design is to appropriate to post 1975 technology. Three candidate architectures are discussed and assessed in terms of the above qualities. Of the three candidates, a newly conceived architecture, Software Implemented Fault Tolerance (SIFT), provides the best match to the above qualities. In addition SIFT is particularly simple and believable. The other candidates, Bus Checker System (BUCS), also newly conceived in this project, and the Hopkins multiprocessor are potentially more efficient than SIFT in the use of redundancy, but otherwise are not as attractive
A Conserved Bach Current
The Bach tensor and a vector which generates conformal symmetries allow a
conserved four-current to be defined. The Bach four-current gives rise to a
quasilocal two-surface expression for power per luminosity distance in the
Vaidya exterior of collapsing fluid interiors. This is interpreted in terms of
entropy generation.Comment: to appear in Class. Quantum Gra
On Rank Problems for Planar Webs and Projective Structures
We present old and recent results on rank problems and linearizability of
geodesic planar webs.Comment: 31 pages; LaTeX; corrected the abstract and Introduction; added
reference
Behaviour of spin-1/2 particle around a charged black hole
Dirac equation is separable in curved space-time and its solution was found
for both spherically and axially symmetric geometry. But most of the works were
done without considering the charge of the black hole. Here we consider the
spherically symmetric charged black hole background namely Reissner-Nordstrom
black hole. Due to presence of the charge of black-hole charge-charge
interaction will be important for the cases of incoming charged particle (e.g.
electron, proton etc.). Therefore both gravitational and electromagnetic gauge
fields should be introduced. Naturally behaviour of the particle will be
changed from that in Schwarzschild geometry. We compare both the solutions. In
the case of Reissner-Nordstrom black hole there is a possibility of
super-radiance unlike Schwarzschild case. We also check this branch of the
solution.Comment: 8 Latex pages and 4 Figures; RevTex.style; Accepted for Publication
in Classical and Quantum Gravit
Higher Spin Field Equation in a Virtual Black Hole Metric
In a quantum theory of gravity, fluctuations about the vacuum may be
considered as Planck scale virtual black holes appearing and annihilating in
pairs. Incident fields scattering from such fluctuations would lose quantum
coherence.
In a recent paper (hep-th/9705147), Hawking and Ross obtained an estimate for
the magnitude of this loss in the case of a scalar field. Their calculation
exploited the separability of the conformally invariant scalar wave equation in
the electrovac C metric background, which is justified as a sufficiently good
description of a virtual black hole pair in the limit considered.
In anticipation of extending this result, the Teukolsky equations for
incident fields of higher spin are separated on the vacuum C metric background
and solved in the same limit. With the exception of spin 2 fields, these
equations are shown in addition to be valid on the electrovac C metric
background. The angular solutions are found to reduce to the spin- weighted
spherical harmonics, and the radial solutions are found to approach
hypergeometrics close to the horizons.
By defining appropriate scattering boundary conditions, these solutions are
then used to estimate the transmission and reflection coefficients for an
incident field of spin s. The transmission coefficient is required in order to
estimate the loss of quantum coherence of an incident field through scattering
off virtual black holes.Comment: 23 pages, 3 figures, LaTeX, minor typo correcte
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