2,991 research outputs found
Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?
We discuss Coleman's theorem concerning the energy density of the ground
state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975).
According to this theorem the energy density of the ground state of the
sine-Gordon model should be unbounded from below for coupling constants beta^2
> 8 pi. The consequence of this theorem would be the non-existence of the
quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that
the energy density of the ground state in the sine-Gordon model is bounded from
below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's
theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and
soliton-soliton scattering in the sine-Gordon model.Comment: 22 pages, Latex, no figures, revised according to the version
accepted for publication in Journal of Physics
Filling the holes: Evolving excised binary black hole initial data with puncture techniques
We follow the inspiral and merger of equal-mass black holes (BHs) by the
moving puncture technique and demonstrate that both the exterior solution and
the asymptotic gravitational waveforms are unchanged when the initial interior
solution is replaced by constraint-violating ``junk'' initial data. We apply
this result to evolve conformal thin-sandwich (CTS) binary BH initial data by
filling their excised interiors with arbitrary, but smooth, initial data and
evolving with standard puncture gauge choices. The waveforms generated for both
puncture and filled-CTS initial data are remarkably similar, and there are only
minor differences between irrotational and corotational CTS BH binaries. Even
the interior solutions appear to evolve to the same constraint-satisfying
solution at late times, independent of the initial data.Comment: 5 pages, 5 figures, accepted by PRD Rapid Communications, RevTe
Quasiequilibrium sequences of black-hole--neutron-star binaries in general relativity
We construct quasiequilibrium sequences of black hole-neutron star binaries
for arbitrary mass ratios by solving the constraint equations of general
relativity in the conformal thin-sandwich decomposition. We model the neutron
star as a stationary polytrope satisfying the relativistic equations of
hydrodynamics, and account for the black hole by imposing equilibrium boundary
conditions on the surface of an excised sphere (the apparent horizon). In this
paper we focus on irrotational configurations, meaning that both the neutron
star and the black hole are approximately nonspinning in an inertial frame. We
present results for a binary with polytropic index n=1, mass ratio
M_{irr}^{BH}/M_{B}^{NS}=5 and neutron star compaction
M_{ADM,0}^{NS}/R_0=0.0879, where M_{irr}^{BH} is the irreducible mass of the
black hole, M_{B}^{NS} the neutron star baryon rest-mass, and M_{ADM,0}^{NS}
and R_0 the neutron star Arnowitt-Deser-Misner mass and areal radius in
isolation, respectively. Our models represent valid solutions to Einstein's
constraint equations and may therefore be employed as initial data for
dynamical simulations of black hole-neutron star binaries.Comment: 5 pages, 1 figure, revtex4, published in Phys.Rev.
Quasiequilibrium black hole-neutron star binaries in general relativity
We construct quasiequilibrium sequences of black hole-neutron star binaries
in general relativity. We solve Einstein's constraint equations in the
conformal thin-sandwich formalism, subject to black hole boundary conditions
imposed on the surface of an excised sphere, together with the relativistic
equations of hydrostatic equilibrium. In contrast to our previous calculations
we adopt a flat spatial background geometry and do not assume extreme mass
ratios. We adopt a Gamma=2 polytropic equation of state and focus on
irrotational neutron star configurations as well as approximately nonspinning
black holes. We present numerical results for ratios of the black hole's
irreducible mass to the neutron star's ADM mass in isolation of
M_{irr}^{BH}/M_{ADM,0}^{NS} = 1, 2, 3, 5, and 10. We consider neutron stars of
baryon rest mass M_B^{NS}/M_B^{max} = 83% and 56%, where M_B^{max} is the
maximum allowed rest mass of a spherical star in isolation for our equation of
state. For these sequences, we locate the onset of tidal disruption and, in
cases with sufficiently large mass ratios and neutron star compactions, the
innermost stable circular orbit. We compare with previous results for black
hole-neutron star binaries and find excellent agreement with third-order
post-Newtonian results, especially for large binary separations. We also use
our results to estimate the energy spectrum of the outgoing gravitational
radiation emitted during the inspiral phase for these binaries.Comment: 17 pages, 15 figures, published in Phys. Rev.
Importance of cooling in triggering the collapse of hypermassive neutron stars
The inspiral and merger of a binary neutron star (NSNS) can lead to the
formation of a hypermassive neutron star (HMNS). As the HMNS loses thermal
pressure due to neutrino cooling and/or centrifugal support due to
gravitational wave (GW) emission, and/or magnetic breaking of differential
rotation it will collapse to a black hole. To assess the importance of
shock-induced thermal pressure and cooling, we adopt an idealized equation of
state and perform NSNS simulations in full GR through late inspiral, merger,
and HMNS formation, accounting for cooling. We show that thermal pressure
contributes significantly to the support of the HMNS against collapse and that
thermal cooling accelerates its "delayed" collapse. Our simulations demonstrate
explicitly that cooling can induce the catastrophic collapse of a hot
hypermassive neutron star formed following the merger of binary neutron stars.
Thus, cooling physics is important to include in NSNS merger calculations to
accurately determine the lifetime of the HMNS remnant and to extract
information about the NS equation of state, cooling mechanisms, bar
instabilities and B-fields from the GWs emitted during the transient phase
prior to BH formation.Comment: 13 pages, 7 figures, matches published versio
The Finite Field Kakeya Problem
A Besicovitch set in AG(n,q) is a set of points containing a line in every
direction. The Kakeya problem is to determine the minimal size of such a set.
We solve the Kakeya problem in the plane, and substantially improve the known
bounds for n greater than 4.Comment: 13 page
Hydro-without-Hydro Framework for Simulations of Black Hole-Neutron Star Binaries
We introduce a computational framework which avoids solving explicitly
hydrodynamic equations and is suitable to study the pre-merger evolution of
black hole-neutron star binary systems. The essence of the method consists of
constructing a neutron star model with a black hole companion and freezing the
internal degrees of freedom of the neutron star during the course of the
evolution of the space-time geometry. We present the main ingredients of the
framework, from the formulation of the problem to the appropriate computational
techniques to study these binary systems. In addition, we present numerical
results of the construction of initial data sets and evolutions that
demonstrate the feasibility of this approach.Comment: 16 pages, 7 figures. To appear in the Classical and Quantum Gravity
special issue on Numerical Relativit
Supernovae in Early-Type Galaxies: Directly Connecting Age and Metallicity with Type Ia Luminosity
We have obtained optical spectra of 29 early-type (E/S0) galaxies that hosted
type Ia supernovae (SNe Ia). We have measured absorption-line strengths and
compared them to a grid of models to extract the relations between the
supernova properties and the luminosity-weighted age/composition of the host
galaxies. The same analysis was applied to a large number of early-type field
galaxies selected from the SDSS spectroscopic survey. We find no difference in
the age and abundance distributions between the field galaxies and the SN Ia
host galaxies. We do find a strong correlation suggesting that SNe Ia in
galaxies whose populations have a characteristic age greater than 5 Gyr are ~ 1
mag fainter at V(max) than those found in galaxies with younger populations.
However, the data cannot discriminate between a smooth relation connecting age
and supernova luminosity or two populations of SN Ia progenitors. We find that
SN Ia distance residuals in the Hubble diagram are correlated with host-galaxy
metal abundance, consistent with the predictions of Timmes, Brown & Truran
(2003). The data show that high iron abundance galaxies host less-luminous
supernovae. We thus conclude that the time since progenitor formation primarily
determines the radioactive Ni production while progenitor metal abundance has a
weaker influence on peak luminosity, but one not fully corrected by light-curve
shape and color fitters. Assuming no selection effects in discovering SNe Ia in
local early-type galaxies, we find a higher specific SN Ia rate in E/S0
galaxies with ages below 3 Gyr than in older hosts. The higher rate and
brighter luminosities seen in the youngest E/S0 hosts may be a result of recent
star formation and represents a tail of the "prompt" SN Ia progenitors.Comment: 44 pages, 11 figures, 4 tables; ApJ Accepted (Sept. 20, 2008 issue
Stable gravastars with generalised exteriors
New spherically symmetric gravastar solutions, stable to radial
perturbations, are found by utilising the construction of Visser and Wiltshire.
The solutions possess an anti--de Sitter or de Sitter interior and a
Schwarzschild--(anti)--de Sitter or Reissner--Nordstr\"{o}m exterior. We find a
wide range of parameters which allow stable gravastar solutions, and present
the different qualitative behaviours of the equation of state for these
parameters.Comment: 14 pages, 11 figures, to appear in Classical and Quantum Gravit
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