206 research outputs found
How the Jones Polynomial Gives Rise to Physical States of Quantum General Relativity
Solutions to both the diffeomorphism and the hamiltonian constraint of
quantum gravity have been found in the loop representation, which is based on
Ashtekar's new variables. While the diffeomorphism constraint is easily solved
by considering loop functionals which are knot invariants, there remains the
puzzle why several of the known knot invariants are also solutions to the
hamiltonian constraint. We show how the Jones polynomial gives rise to an
infinite set of solutions to all the constraints of quantum gravity thereby
illuminating the structure of the space of solutions and suggesting the
existance of a deep connection between quantum gravity and knot theory at a
dynamical level.Comment: 7p
Adaptive mesh and geodesically sliced Schwarzschild spacetime in 3+1 dimensions
We present first results obtained with a 3+1 dimensional adaptive mesh code
in numerical general relativity. The adaptive mesh is used in conjunction with
a standard ADM code for the evolution of a dynamically sliced Schwarzschild
spacetime (geodesic slicing). We argue that adaptive mesh is particularly
natural in the context of general relativity, where apart from adaptive mesh
refinement for numerical efficiency one may want to use the built in
flexibility to do numerical relativity on coordinate patches.Comment: 21 pages, LaTeX, 7 figures included with eps
A single-domain spectral method for black hole puncture data
We calculate puncture initial data corresponding to both single and binary
black hole solutions of the constraint equations by means of a pseudo-spectral
method applied in a single spatial domain. Introducing appropriate coordinates,
these methods exhibit rapid convergence of the conformal factor and lead to
highly accurate solutions. As an application we investigate small mass ratios
of binary black holes and compare these with the corresponding test mass limit
that we obtain through a semi-analytical limiting procedure. In particular, we
compare the binding energy of puncture data in this limit with that of a test
particle in the Schwarzschild spacetime and find that it deviates by 50% from
the Schwarzschild result at the innermost stable circular orbit of
Schwarzschild, if the ADM mass at each puncture is used to define the local
black hole masses.Comment: 13 pages, 6 figures; published version with one important change, see
Fig. 4 and the corresponding changes to the tex
Beyond the Bowen-York extrinsic curvature for spinning black holes
It is well-known that Bowen-York initial data contain spurious radiation.
Although this ``junk'' radiation has been seen to be small for non-spinning
black-hole binaries in circular orbit, its magnitude increases when the black
holes are given spin. It is possible to reduce the spurious radiation by
applying the puncture approach to multiple Kerr black holes, as we demonstrate
for examples of head-on collisions of equal-mass black-hole binaries.Comment: 10 pages, 2 figures, submitted to special "New Frontiers in Numerical
Relativity" issue of Classical and Quantum Gravit
Traces of ancient mafic layers in the Tethys oceanic mantle
Oceanic basalts are formed by melting of a chemically and isotopically heterogeneous mantle source. The oceanic mantle probably resembles a marble cake containing layers of mafic rock - perhaps recycled ocean crust - stored in the mantle for >1 billion years. Many questions about the nature and distribution of these mantle heterogeneities remain. Here we show that lithological and isotopic traces of ancient mafic layers can still be seen in mantle rocks that have melted to form oceanic crust at a spreading centre in the Tethys Ocean. We have found centimetre-scale heterogeneity in initial osmium isotope ratios in mantle rocks from the Pindos Ophiolite. Deformed pyroxenite layers have high 187Os/188Os ratios (0.14-0.20) compared to adjacent host peridotites (187Os/188Os: 0.12-0.13). These layers were formed by a reaction between mantle rock and melt derived from ancient rocks with high Re/Os ratios. We interpret the pyroxenite layers as the wall rocks of billion-year old mafic layers that melted and transformed adjacent mantle peridotite into pyroxenite by melt-rock reaction. The pyroxenite layers are the relics of ancient metre-scale basaltic veins in a kilometre-sized marble cake domain in the oceanic mantle that has withstood homogenization on a billion-year time scale. © 2013
Quasi-equilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions
We construct a sequence of binary black hole puncture data derived under the
assumptions (i) that the ADM mass of each puncture as measured in the
asymptotically flat space at the puncture stays constant along the sequence,
and (ii) that the orbits along the sequence are quasi-circular in the sense
that several necessary conditions for the existence of a helical Killing vector
are satisfied. These conditions are equality of ADM and Komar mass at infinity
and equality of the ADM and a rescaled Komar mass at each puncture. In this
paper we explicitly give results for the case of an equal mass black hole
binary without spin, but our approach can also be applied in the general case.
We find that up to numerical accuracy the apparent horizon mass also remains
constant along the sequence and that the prediction for the innermost stable
circular orbit is similar to what has been found with the effective potential
method.Comment: 6 pages, 3 figures, 1 tabl
Binary black hole initial data from matched asymptotic expansions
We present an approximate metric for a binary black hole spacetime to
construct initial data for numerical relativity. This metric is obtained by
asymptotically matching a post-Newtonian metric for a binary system to a
perturbed Schwarzschild metric for each hole. In the inner zone near each hole,
the metric is given by the Schwarzschild solution plus a quadrupolar
perturbation corresponding to an external tidal gravitational field. In the
near zone, well outside each black hole but less than a reduced wavelength from
the center of mass of the binary, the metric is given by a post-Newtonian
expansion including the lowest-order deviations from flat spacetime. When the
near zone overlaps each inner zone in a buffer zone, the post-Newtonian and
perturbed Schwarzschild metrics can be asymptotically matched to each other. By
demanding matching (over a 4-volume in the buffer zone) rather than patching
(choosing a particular 2-surface in the buffer zone), we guarantee that the
errors are small in all zones. The resulting piecewise metric is made formally
with smooth transition functions so as to obtain the finite
extrinsic curvature of a 3-slice. In addition to the metric and extrinsic
curvature, we present explicit results for the lapse and the shift, which can
be used as initial data for numerical simulations. This initial data is not
accurate all the way to the asymptotically flat ends inside each hole, and
therefore must be used with evolution codes which employ black hole excision
rather than puncture methods. This paper lays the foundations of a method that
can be sraightforwardly iterated to obtain initial data to higher perturbative
order.Comment: 24 pages, 15 figures. Replaced with published version. Major editing
of text, no major change to the physic
Binary black hole initial data for numerical general relativity based on post-Newtonian data
With the goal of taking a step toward the construction of astrophysically
realistic initial data for numerical simulations of black holes, we for the
first time derive a family of fully general relativistic initial data based on
post-2-Newtonian expansions of the 3-metric and extrinsic curvature without
spin. It is expected that such initial data provide a direct connection with
the early inspiral phase of the binary system. We discuss a straightforward
numerical implementation, which is based on a generalized puncture method.
Furthermore, we suggest a method to address some of the inherent ambiguity in
mapping post-Newtonian data onto a solution of the general relativistic
constraints.Comment: 13 pages, 8 figures, RevTex
Numerical evolution of multiple black holes with accurate initial data
We present numerical evolutions of three equal-mass black holes using the
moving puncture approach. We calculate puncture initial data for three black
holes solving the constraint equations by means of a high-order multigrid
elliptic solver. Using these initial data, we show the results for three black
hole evolutions with sixth-order waveform convergence. We compare results
obtained with the BAM and AMSS-NCKU codes with previous results. The
approximate analytic solution to the Hamiltonian constraint used in previous
simulations of three black holes leads to different dynamics and waveforms. We
present some numerical experiments showing the evolution of four black holes
and the resulting gravitational waveform.Comment: Published in PR
Plunge waveforms from inspiralling binary black holes
We study the coalescence of non-spinning binary black holes from near the
innermost stable circular orbit down to the final single rotating black hole.
We use a technique that combines the full numerical approach to solve Einstein
equations, applied in the truly non-linear regime, and linearized perturbation
theory around the final distorted single black hole at later times. We compute
the plunge waveforms which present a non negligible signal lasting for showing early non-linear ringing, and we obtain estimates for the total
gravitational energy and angular momentum radiated.Comment: Corrected typos in the radiated ang momentum and frequenc
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