2,133 research outputs found
Explicit solution of the linearized Einstein equations in TT gauge for all multipoles
We write out the explicit form of the metric for a linearized gravitational
wave in the transverse-traceless gauge for any multipole, thus generalizing the
well-known quadrupole solution of Teukolsky. The solution is derived using the
generalized Regge-Wheeler-Zerilli formalism developed by Sarbach and Tiglio.Comment: 9 pages. Minor corrections, updated references. Final version to
appear in Class. Quantum Gra
Symmetric hyperbolic system in the Ashtekar formulation
We present a first-order symmetric hyperbolic system in the Ashtekar
formulation of general relativity for vacuum spacetime. We add terms from
constraint equations to the evolution equations with appropriate combinations,
which is the same technique used by Iriondo, Leguizam\'on and Reula [Phys. Rev.
Lett. 79, 4732 (1997)]. However our system is different from theirs in the
points that we primarily use Hermiticity of a characteristic matrix of the
system to characterize our system "symmetric", discuss the consistency of this
system with reality condition, and show the characteristic speeds of the
system.Comment: 4 pages, RevTeX, to appear in Phys. Rev. Lett., Comments added, refs
update
Spontaneous decay of an excited atom in an absorbing dielectric
Starting from the quantized version of Maxwell's equations for the
electromagnetic field in an arbitrary linear Kramers-Kronig dielectric,
spontaneous decay of the excited state of a two-level atom embedded in a
dispersive and absorbing medium is studied and the decay rate is calculated.
The calculations are performed for both the (Clausius-Mosotti) virtual cavity
model and the (Glauber-Lewenstein) real cavity model. It is shown that owing to
nonradiative decay associated with absorption the rate of spontaneous decay
sensitively depends on the cavity radius when the atomic transition frequency
approaches an absorption band of the medium. Only when the effect of absorption
is fully disregarded, then the familiar local-field correction factors are
recovered.Comment: 28 pages, 6 figures, typeset using RevTe
Energy Norms and the Stability of the Einstein Evolution Equations
The Einstein evolution equations may be written in a variety of equivalent
analytical forms, but numerical solutions of these different formulations
display a wide range of growth rates for constraint violations. For symmetric
hyperbolic formulations of the equations, an exact expression for the growth
rate is derived using an energy norm. This expression agrees with the growth
rate determined by numerical solution of the equations. An approximate method
for estimating the growth rate is also derived. This estimate can be evaluated
algebraically from the initial data, and is shown to exhibit qualitatively the
same dependence as the numerically-determined rate on the parameters that
specify the formulation of the equations. This simple rate estimate therefore
provides a useful tool for finding the most well-behaved forms of the evolution
equations.Comment: Corrected typos; to appear in Physical Review
Collapse to Black Holes in Brans-Dicke Theory: I. Horizon Boundary Conditions for Dynamical Spacetimes
We present a new numerical code that evolves a spherically symmetric
configuration of collisionless matter in the Brans-Dicke theory of gravitation.
In this theory the spacetime is dynamical even in spherical symmetry, where it
can contain gravitational radiation. Our code is capable of accurately tracking
collapse to a black hole in a dynamical spacetime arbitrarily far into the
future, without encountering either coordinate pathologies or spacetime
singularities. This is accomplished by truncating the spacetime at a spherical
surface inside the apparent horizon, and subsequently solving the evolution and
constraint equations only in the exterior region. We use our code to address a
number of long-standing theoretical questions about collapse to black holes in
Brans-Dicke theory.Comment: 46 pages including figures, uuencoded gz-compressed postscript,
Submitted to Phys Rev
Biogeography and taxonomy of extinct and endangered monk seals illuminated by ancient DNA and skull morphology
Extinctions and declines of large marine vertebrates have major ecological impacts and are of critical concern in marine environments. The Caribbean monk seal, Monachus tropicalis, last definitively reported in 1952, was one of the few marine mammal species to become extinct in historical times. Despite its importance for understanding the evolutionary biogeography of southern phocids, the relationships of M. tropicalis to the two living species of critically endangered monk seals have not been resolved. In this study we present the first molecular data for M. tropicalis, derived from museum skins. Phylogenetic analysis of cytochrome b sequences indicates that M. tropicalis was more closely related to the Hawaiian rather than the Mediterranean monk seal. Divergence time estimation implicates the formation of the Panamanian Isthmus in the speciation of Caribbean and Hawaiian monk seals. Molecular, morphological and temporal divergence between the Mediterranean and "New World monk seals" (Hawaiian and Caribbean) is profound, equivalent to or greater than between sister genera of phocids. As a result, we classify the Caribbean and Hawaiian monk seals together in a newly erected genus, Neomonachus. The two genera of extant monk seals (Monachus and Neomonachus) represent old evolutionary lineages each represented by a single critically endangered species, both warranting continuing and concerted conservation attention and investment if they are to avoid the fate of their Caribbean relative.Dirk-Martin Scheel, Graham J. Slater, Sergios-Orestis Kolokotronis, Charles W. Potter, David S. Rotstein, Kyriakos Tsangaras, Alex D. Greenwood, Kristofer M. Helge
Evolving Einstein's Field Equations with Matter: The ``Hydro without Hydro'' Test
We include matter sources in Einstein's field equations and show that our
recently proposed 3+1 evolution scheme can stably evolve strong-field
solutions. We insert in our code known matter solutions, namely the
Oppenheimer-Volkoff solution for a static star and the Oppenheimer-Snyder
solution for homogeneous dust sphere collapse to a black hole, and evolve the
gravitational field equations. We find that we can evolve stably static,
strong-field stars for arbitrarily long times and can follow dust sphere
collapse accurately well past black hole formation. These tests are useful
diagnostics for fully self-consistent, stable hydrodynamical simulations in 3+1
general relativity. Moreover, they suggest a successive approximation scheme
for determining gravitational waveforms from strong-field sources dominated by
longitudinal fields, like binary neutron stars: approximate quasi-equilibrium
models can serve as sources for the transverse field equations, which can be
evolved without having to re-solve the hydrodynamical equations (``hydro
without hydro'').Comment: 4 postscript figures. Submitted to Phys. Rev. D15 as a Brief Repor
Implementing an apparent-horizon finder in three dimensions
Locating apparent horizons is not only important for a complete understanding
of numerically generated spacetimes, but it may also be a crucial component of
the technique for evolving black-hole spacetimes accurately. A scheme proposed
by Libson et al., based on expanding the location of the apparent horizon in
terms of symmetric trace-free tensors, seems very promising for use with
three-dimensional numerical data sets. In this paper, we generalize this scheme
and perform a number of code tests to fully calibrate its behavior in
black-hole spacetimes similar to those we expect to encounter in solving the
binary black-hole coalescence problem. An important aspect of the
generalization is that we can compute the symmetric trace-free tensor expansion
to any order. This enables us to determine how far we must carry the expansion
to achieve results of a desired accuracy. To accomplish this generalization, we
describe a new and very convenient set of recurrence relations which apply to
symmetric trace-free tensors.Comment: 14 pages (RevTeX 3.0 with 3 figures
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