1,422 research outputs found
Testing post-Newtonian theory with gravitational wave observations
The Laser Interferometric Space Antenna (LISA) will observe supermassive
black hole binary mergers with amplitude signal-to-noise ratio of several
thousands. We investigate the extent to which such observations afford
high-precision tests of Einstein's gravity. We show that LISA provides a unique
opportunity to probe the non-linear structure of post-Newtonian theory both in
the context of general relativity and its alternatives.Comment: 9 pages, 2 figure
Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions
Two long-standing problems with the post-Newtonian approximation for isolated
slowly-moving systems in general relativity are: (i) the appearance at high
post-Newtonian orders of divergent Poisson integrals, casting a doubt on the
soundness of the post-Newtonian series; (ii) the domain of validity of the
approximation which is limited to the near-zone of the source, and prevents
one, a priori, from incorporating the condition of no-incoming radiation, to be
imposed at past null infinity. In this article, we resolve the problem (i) by
iterating the post-Newtonian hierarchy of equations by means of a new
(Poisson-type) integral operator that is free of divergencies, and the problem
(ii) by matching the post-Newtonian near-zone field to the exterior field of
the source, known from previous work as a multipolar-post-Minkowskian expansion
satisfying the relevant boundary conditions at infinity. As a result, we obtain
an algorithm for iterating the post-Newtonian series up to any order, and we
determine the terms, present in the post-Newtonian field, that are associated
with the gravitational-radiation reaction onto an isolated slowly-moving matter
system.Comment: 61 pages, to appear in Phys. Rev.
Post-ISCO Ringdown Amplitudes in Extreme Mass Ratio Inspiral
An extreme mass ratio inspiral consists of two parts: adiabatic inspiral and
plunge. The plunge trajectory from the innermost stable circular orbit (ISCO)
is special (somewhat independent of initial conditions). We write an expression
for its solution in closed-form and for the emitted waveform. In particular we
extract an expression for the associated black-hole ringdown amplitudes, and
evaluate them numerically.Comment: 21 pages, 5 figures. v4: added section with numerical evaluation of
the ringdown amplitude
Alternatives to standard puncture initial data for binary black hole evolution
Standard puncture initial data have been widely used for numerical binary
black hole evolutions despite their shortcomings, most notably the inherent
lack of gravitational radiation at the initial time that is later followed by a
burst of spurious radiation. We study the evolution of three alternative
initial data schemes. Two of the three alternatives are based on post-Newtonian
expansions that contain realistic gravitational waves. The first scheme is
based on a second-order post-Newtonian expansion in Arnowitt, Deser, and Misner
transverse-traceless (ADMTT) gauge that has been resummed to approach standard
puncture data at the black holes. The second scheme is based on asymptotic
matching of the 4-metrics of two tidally perturbed Schwarzschild solutions to a
first-order post-Newtonian expansion in ADMTT gauge away from the black holes.
The final alternative is obtained through asymptotic matching of the 4-metrics
of two tidally perturbed Schwarzschild solutions to a second-order
post-Newtonian expansion in harmonic gauge away from the black holes. When
evolved, the second scheme fails to produce quasicircular orbits (and instead
leads to a nearly head-on collision). This failure can be traced back to
inaccuracies in the extrinsic curvature due to low order matching. More
encouraging is that the latter two alternatives lead to quasicircular orbits
and show gravitational radiation from the onset of the evolution, as well as a
reduction of spurious radiation. Current deficiencies compared to standard
punctures data include more eccentric trajectories during the inspiral and
larger constraint violations, since the alternative data sets are only
approximate solutions of Einstein's equations. The eccentricity problem can be
ameliorated by adjusting the initial momentum parameters.Comment: 11 pages, 11 figures, 1 appendix, typos corrected, removed duplicate
reference, matches published versio
Evolution of Binary Black Hole Spacetimes
We describe early success in the evolution of binary black hole spacetimes
with a numerical code based on a generalization of harmonic coordinates.
Indications are that with sufficient resolution this scheme is capable of
evolving binary systems for enough time to extract information about the orbit,
merger and gravitational waves emitted during the event. As an example we show
results from the evolution of a binary composed of two equal mass, non-spinning
black holes, through a single plunge-orbit, merger and ring down. The resultant
black hole is estimated to be a Kerr black hole with angular momentum parameter
a~0.70. At present, lack of resolution far from the binary prevents an accurate
estimate of the energy emitted, though a rough calculation suggests on the
order of 5% of the initial rest mass of the system is radiated as gravitational
waves during the final orbit and ringdown.Comment: 4 pages, 3 figure
On formal verification of arithmetic-based cryptographic primitives
Cryptographic primitives are fundamental for information security: they are
used as basic components for cryptographic protocols or public-key
cryptosystems. In many cases, their security proofs consist in showing that
they are reducible to computationally hard problems. Those reductions can be
subtle and tedious, and thus not easily checkable. On top of the proof
assistant Coq, we had implemented in previous work a toolbox for writing and
checking game-based security proofs of cryptographic primitives. In this paper
we describe its extension with number-theoretic capabilities so that it is now
possible to write and check arithmetic-based cryptographic primitives in our
toolbox. We illustrate our work by machine checking the game-based proofs of
unpredictability of the pseudo-random bit generator of Blum, Blum and Shub, and
semantic security of the public-key cryptographic scheme of Goldwasser and
Micali.Comment: 13 page
Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order
We compute the radiation reaction force on the orbital motion of compact
binaries to the 3.5 post-Newtonian (3.5PN) approximation, i.e. one PN order
beyond the dominant effect. The method is based on a direct PN iteration of the
near-zone metric and equations of motion of an extended isolated system, using
appropriate ``asymptotically matched'' flat-space-time retarded potentials. The
formalism is subsequently applied to binary systems of point particles, with
the help of the Hadamard self-field regularisation. Our result is the 3.5PN
acceleration term in a general harmonic coordinate frame. Restricting the
expression to the centre-of-mass frame, we find perfect agreement with the
result derived in a class of coordinate systems by Iyer and Will using the
energy and angular momentum balance equations.Comment: 28 pages, references added, to appear in Classical and Quantum
Gravit
Time-dependent photoionization of azulene: Competition between ionization and relaxation in highly excited states
Pump-probe photoionization has been used to map the relaxation processes taking place from highly vibrationally excited levels of the S2 state of azulene, populated directly or via internal conversion from the S4 state. Photoelectron spectra obtained by 1+2’ two-color time-resolved photoelectron imaging are invariant (apart from in intensity) to the pump-probe time delay and to pump wavelength. This reveals a photoionization process which is driven by an unstable electronic state (e.g. doubly excited state) lying below the ionization potential. This state is postulated to be populated by a probe transition from S2 and to rapidly relax via an Auger like process onto highly
vibrationally excited Rydberg states. This accounts for the time invariance of the photoelectron spectrum. The intensity of the photoelectron spectrum is proportional to the population in S2. An exponential energy gap law is used to describe the internal conversion rate from S2 to S0. The
vibronic coupling strength is found to be larger than 60±5 μeV
YAPA: A generic tool for computing intruder knowledge
Reasoning about the knowledge of an attacker is a necessary step in many
formal analyses of security protocols. In the framework of the applied pi
calculus, as in similar languages based on equational logics, knowledge is
typically expressed by two relations: deducibility and static equivalence.
Several decision procedures have been proposed for these relations under a
variety of equational theories. However, each theory has its particular
algorithm, and none has been implemented so far. We provide a generic procedure
for deducibility and static equivalence that takes as input any convergent
rewrite system. We show that our algorithm covers most of the existing decision
procedures for convergent theories. We also provide an efficient
implementation, and compare it briefly with the tools ProVerif and KiSs
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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