32,952 research outputs found
Solving the Darwin problem in the first post-Newtonian approximation of general relativity
We analytically calculate the equilibrium sequence of the corotating binary
stars of incompressible fluid in the first post-Newtonian(PN) approximation of
general relativity. By calculating the total energy and total angular momentum
of the system as a function of the orbital separation, we investigate the
innermost stable circular orbit for corotating binary(we call it ISCCO). It is
found that by the first PN effect, the orbital separation of the binary at the
ISCCO becomes small with increase of the compactness of each star, and as a
result, the orbital angular velocity at the ISCCO increases. These behaviors
agree with previous numerical works.Comment: 33 pages, revtex, 4 figures(eps), accepted for publication in Phys.
Rev.
Innermost Stable Circular Orbit of Inspiraling Neutron-Star Binaries: Tidal Effects, Post-Newtonian Effects and the Neutron-Star Equation of State
We study how the neutron-star equation of state affects the onset of the
dynamical instability in the equations of motion for inspiraling neutron-star
binaries near coalescence. A combination of relativistic effects and Newtonian
tidal effects cause the stars to begin their final, rapid, and
dynamically-unstable plunge to merger when the stars are still well separated
and the orbital frequency is 500 cycles/sec (i.e. the gravitational
wave frequency is approximately 1000 Hz). The orbital frequency at which the
dynamical instability occurs (i.e. the orbital frequency at the innermost
stable circular orbit) shows modest sensitivity to the neutron-star equation of
state (particularly the mass-radius ratio, , of the stars). This
suggests that information about the equation of state of nuclear matter is
encoded in the gravitational waves emitted just prior to the merger.Comment: RevTeX, to appear in PRD, 8 pages, 4 figures include
General-relativistic coupling between orbital motion and internal degrees of freedom for inspiraling binary neutron stars
We analyze the coupling between the internal degrees of freedom of neutron
stars in a close binary, and the stars' orbital motion. Our analysis is based
on the method of matched asymptotic expansions and is valid to all orders in
the strength of internal gravity in each star, but is perturbative in the
``tidal expansion parameter'' (stellar radius)/(orbital separation). At first
order in the tidal expansion parameter, we show that the internal structure of
each star is unaffected by its companion, in agreement with post-1-Newtonian
results of Wiseman (gr-qc/9704018). We also show that relativistic interactions
that scale as higher powers of the tidal expansion parameter produce
qualitatively similar effects to their Newtonian counterparts: there are
corrections to the Newtonian tidal distortion of each star, both of which occur
at third order in the tidal expansion parameter, and there are corrections to
the Newtonian decrease in central density of each star (Newtonian ``tidal
stabilization''), both of which are sixth order in the tidal expansion
parameter. There are additional interactions with no Newtonian analogs, but
these do not change the central density of each star up to sixth order in the
tidal expansion parameter. These results, in combination with previous analyses
of Newtonian tidal interactions, indicate that (i) there are no large
general-relativistic crushing forces that could cause the stars to collapse to
black holes prior to the dynamical orbital instability, and (ii) the
conventional wisdom with respect to coalescing binary neutron stars as sources
of gravitational-wave bursts is correct: namely, the finite-stellar-size
corrections to the gravitational waveform will be unimportant for the purpose
of detecting the coalescences.Comment: 22 pages, 2 figures. Replaced 13 July: proof corrected, result
unchange
Binary-Induced Gravitational Collapse: A Trivial Example
We present a simple model illustrating how a highly relativistic, compact
object which is stable in isolation can be driven dynamically unstable by the
tidal field of a binary companion. Our compact object consists of a
test-particle in a relativistic orbit about a black hole; the binary companion
is a distant point mass. Our example is presented in light of mounting
theoretical opposition to the possibility that sufficiently massive, binary
neutron stars inspiraling from large distance can collapse to form black holes
prior to merger. Our strong-field model suggests that first order
post-Newtonian treatments of binaries, and stability analyses of binary
equilibria based on orbit-averaged, mean gravitational fields, may not be
adequate to rule out this possibility.Comment: 7 pages, 5 figures, RevTeX, to appear in Phys. Rev. D, Jan 15 199
Black Hole Production by Cosmic Rays
Ultra-high energy cosmic rays create black holes in scenarios with extra
dimensions and TeV-scale gravity. In particular, cosmic neutrinos will produce
black holes deep in the atmosphere, initiating quasi-horizontal showers far
above the standard model rate. At the Auger Observatory, hundreds of black hole
events may be observed, providing evidence for extra dimensions and the first
opportunity for experimental study of microscopic black holes. If no black
holes are found, the fundamental Planck scale must be above 2 TeV for any
number of extra dimensions.Comment: 4 pages, 4 figures, PRL versio
Post-Newtonian Models of Binary Neutron Stars
Using an energy variational method, we calculate quasi-equilibrium
configurations of binary neutron stars modeled as compressible triaxial
ellipsoids obeying a polytropic equation of state. Our energy functional
includes terms both for the internal hydrodynamics of the stars and for the
external orbital motion. We add the leading post-Newtonian (PN) corrections to
the internal and gravitational energies of the stars, and adopt hybrid orbital
terms which are fully relativistic in the test-mass limit and always accurate
to PN order. The total energy functional is varied to find quasi-equilibrium
sequences for both corotating and irrotational binaries in circular orbits. We
examine how the orbital frequency at the innermost stable circular orbit
depends on the polytropic index n and the compactness parameter GM/Rc^2. We
find that, for a given GM/Rc^2, the innermost stable circular orbit along an
irrotational sequence is about 17% larger than the innermost secularly stable
circular orbit along the corotating sequence when n=0.5, and 20% larger when
n=1. We also examine the dependence of the maximum neutron star mass on the
orbital frequency and find that, if PN tidal effects can be neglected, the
maximum equilibrium mass increases as the orbital separation decreases.Comment: 53 pages, LaTex, 9 figures as 10 postscript files, accepted by Phys.
Rev. D, replaced version contains updated reference
Quasi-Local Energy Flux of Spacetime Perturbation
A general expression for quasi-local energy flux for spacetime perturbation
is derived from covariant Hamiltonian formulation using functional
differentiability and symplectic structure invariance, which is independent of
the choice of the canonical variables and the possible boundary terms one
initially puts into the Lagrangian in the diffeomorphism invariant theories.
The energy flux expression depends on a displacement vector field and the
2-surface under consideration. We apply and test the expression in Vaidya
spacetime. At null infinity the expression leads to the Bondi type energy flux
obtained by Lindquist, Schwartz and Misner. On dynamical horizons with a
particular choice of the displacement vector, it gives the area balance law
obtained by Ashtekar and Krishnan.Comment: 8 pages, added appendix, version to appear in Phys. Rev.
Strange nonchaotic attractors in noise driven systems
Strange nonchaotic attractors (SNAs) in noise driven systems are
investigated. Before the transition to chaos, due to the effect of noise, a
typical trajectory will wander between the periodic attractor and its nearby
chaotic saddle in an intermittent way, forms a strange attractor gradually. The
existence of SNAs is confirmed by simulation results of various critera both in
map and continuous systems. Dimension transition is found and intermittent
behavior is studied by peoperties of local Lyapunov exponent. The universality
and generalization of this kind of SNAs are discussed and common features are
concluded
Pilot, Rollout and Monte Carlo Tree Search Methods for Job Shop Scheduling
Greedy heuristics may be attuned by looking ahead for each possible choice,
in an approach called the rollout or Pilot method. These methods may be seen as
meta-heuristics that can enhance (any) heuristic solution, by repetitively
modifying a master solution: similarly to what is done in game tree search,
better choices are identified using lookahead, based on solutions obtained by
repeatedly using a greedy heuristic. This paper first illustrates how the Pilot
method improves upon some simple well known dispatch heuristics for the
job-shop scheduling problem. The Pilot method is then shown to be a special
case of the more recent Monte Carlo Tree Search (MCTS) methods: Unlike the
Pilot method, MCTS methods use random completion of partial solutions to
identify promising branches of the tree. The Pilot method and a simple version
of MCTS, using the -greedy exploration paradigms, are then
compared within the same framework, consisting of 300 scheduling problems of
varying sizes with fixed-budget of rollouts. Results demonstrate that MCTS
reaches better or same results as the Pilot methods in this context.Comment: Learning and Intelligent OptimizatioN (LION'6) 7219 (2012
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