157 research outputs found
On the constraint algebra of quantum gravity in the loop representation
Although an important issue in canonical quantization, the problem of
representing the constraint algebra in the loop representation of quantum
gravity has received little attention. The only explicit computation was
performed by Gambini, Garat and Pullin for a formal point-splitting
regularization of the diffeomorphism and Hamiltonian constraints. It is shown
that the calculation of the algebra simplifies considerably when the
constraints are expressed not in terms of generic area derivatives but rather
as the specific shift operators that reflect the geometric meaning of the
constraints.Comment: 17 pages, LaTeX, 2 figures included with eps
Spinning black hole in the puncture method: Numerical experiments
The strong-field region inside a black hole needs special attention during numerical simulation. One approach for handling the problem is the moving puncture method, which has become an important tool in numerical relativity since it allows long term simulations of binary black holes. An essential component of this method is the choice of the '1+log'-slicing condition. We present an investigation of this slicing condition in rotating black hole spacetimes. We discuss how the results of the stationary Schwarzschild '1+log'-trumpet change when spin is added. This modification enables a simple and cheap algorithm for determining the spin of a non-moving black hole for this particular slicing condition. Applicability of the algorithm is verified in simulations of single black hole, binary neutron star and mixed binary simulations
Monte Carlo simulations of 4d simplicial quantum gravity
Dynamical triangulations of four-dimensional Euclidean quantum gravity give
rise to an interesting, numerically accessible model of quantum gravity. We
give a simple introduction to the model and discuss two particularly important
issues. One is that contrary to recent claims there is strong analytical and
numerical evidence for the existence of an exponential bound that makes the
partition function well-defined. The other is that there may be an ambiguity in
the choice of the measure of the discrete model which could even lead to the
existence of different universality classes.Comment: 16 pages, LaTeX, epsf, 4 uuencoded figures; contribution to the JMP
special issue on "Quantum Geometry and Diffeomorphism-Invariant Quantum Field
Theory
Comparison between numerical relativity and a new class of post-Newtonian gravitational-wave phase evolutions: the non-spinning equal-mass case
We compare the phase evolution of equal-mass nonspinning black-hole binaries
from numerical relativity (NR) simulations with post-Newtonian (PN) results
obtained from three PN approximants: the TaylorT1 and T4 approximants, for
which NR-PN comparisons have already been performed in the literature, and the
recently proposed approximant TaylorEt. The accumulated phase disagreement
between NR and PN results over the frequency range to
is greater for TaylorEt than either T1 or T4, but has the
attractive property of decreasing monotonically as the PN order is increased.Comment: 6 pages, 4 figure
More on the exponential bound of four dimensional simplicial quantum gravity
A crucial requirement for the standard interpretation of Monte Carlo
simulations of simplicial quantum gravity is the existence of an exponential
bound that makes the partition function well-defined. We present numerical data
favoring the existence of an exponential bound, and we argue that the more
limited data sets on which recently opposing claims were based are also
consistent with the existence of an exponential bound.Comment: 10 pages, latex, 2 figure
High-spin binary black hole mergers
We study identical mass black hole binaries with spins perpendicular to the
binary's orbital plane. These binaries have individual spins ranging from
to 0.90, ( in all cases) which is near the limit
possible with standard Bowen-York puncture initial data. The extreme cases
correspond to the largest initial spin simulations to date. Our results expand
the parameter space covered by Rezzolla {\it et al.} and, when combining both
data sets, we obtain estimations for the minimum and maximum values for the
intrinsic angular momenta of the remnant of binary black hole mergers of
and respectively. Note, however, that
these values are reached through extrapolation to the singular cases and thus remain as {\it estimates} until full-fledged numerical
simulations provide confirmation.Comment: 8 pages, 7 figures. Changed to match the version accepted for
publication in PR
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
Binary Black Hole Mergers in 3d Numerical Relativity
The standard approach to the numerical evolution of black hole data using the
ADM formulation with maximal slicing and vanishing shift is extended to
non-symmetric black hole data containing black holes with linear momentum and
spin by using a time-independent conformal rescaling based on the puncture
representation of the black holes. We give an example for a concrete three
dimensional numerical implementation. The main result of the simulations is
that this approach allows for the first time to evolve through a brief period
of the merger phase of the black hole inspiral.Comment: 8 pages, 9 figures, REVTeX; expanded discussion, results unchange
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