3,336 research outputs found
Numerical implementation of isolated horizon boundary conditions
We study the numerical implementation of a set of boundary conditions derived
from the isolated horizon formalism, and which characterize a black hole whose
horizon is in quasi-equilibrium. More precisely, we enforce these geometrical
prescriptions as inner boundary conditions on an excised sphere, in the
numerical resolution of the Conformal Thin Sandwich equations. As main results,
we firstly establish the consistency of including in the set of boundary
conditions a "constant surface gravity" prescription, interpretable as a lapse
boundary condition, and secondly we assess how the prescriptions presented
recently by Dain et al. for guaranteeing the well-posedness of the Conformal
Transverse Traceless equations with quasi-equilibrium horizon conditions extend
to the Conformal Thin Sandwich elliptic system. As a consequence of the latter
analysis, we discuss the freedom of prescribing the expansion associated with
the ingoing null normal at the horizon.Comment: 11 pages, 5 figures, references added and correcte
Nonabelian gauge field dynamics on matrix D-branes
We construct a calculational scheme for handling the matrix ordering problems
connected with the appearance of D-brane positions taking values in the same
Lie algebra as the nonabelian gauge field living on the D-brane. The formalism
is based on the use of an one-dimensional auxiliary field living on the
boundary of the string world sheet and taking care of the order of the matrix
valued fields. The resulting system of equations of motion for both the gauge
field and the D-brane position is derived in lowest order of the
-expansion.Comment: 14 pages, Latex, 2 figures, including epsfig.sty, a wrong reference
number correcte
Equilibrium initial data for moving puncture simulations: The stationary 1+log slicing
We propose and explore a "stationary 1+log" slicing condition for the
construction of solutions to Einstein's constraint equations. For stationary
spacetimes, these initial data will give a stationary foliation when evolved
with "moving puncture" gauge conditions that are often used in black hole
evolutions. The resulting slicing is time-independent and agrees with the
slicing generated by being dragged along a time-like Killing vector of the
spacetime. When these initial data are evolved with moving puncture gauge
conditions, numerical errors arising from coordinate evolution are minimized.
In the construction of initial data for binary black holes it is often assumed
that there exists an approximate helical Killing vector that generates the
binary's orbit. We show that, unfortunately, 1+log slices that are stationary
with respect to such a helical Killing vector cannot be asymptotically flat,
unless the spacetime possesses an additional axial Killing vector.Comment: 20 pages, 3 figures, published versio
Dynamically Triangulating Lorentzian Quantum Gravity
Fruitful ideas on how to quantize gravity are few and far between. In this
paper, we give a complete description of a recently introduced non-perturbative
gravitational path integral whose continuum limit has already been investigated
extensively in d less than 4, with promising results. It is based on a
simplicial regularization of Lorentzian space-times and, most importantly,
possesses a well-defined, non-perturbative Wick rotation. We present a detailed
analysis of the geometric and mathematical properties of the discretized model
in d=3,4. This includes a derivation of Lorentzian simplicial manifold
constraints, the gravitational actions and their Wick rotation. We define a
transfer matrix for the system and show that it leads to a well-defined
self-adjoint Hamiltonian. In view of numerical simulations, we also suggest
sets of Lorentzian Monte Carlo moves. We demonstrate that certain pathological
phases found previously in Euclidean models of dynamical triangulations cannot
be realized in the Lorentzian case.Comment: 41 pages, 14 figure
Measuring eccentricity in binary black-hole initial data
Initial data for evolving black-hole binaries can be constructed via many
techniques, and can represent a wide range of physical scenarios. However,
because of the way that different schemes parameterize the physical aspects of
a configuration, it is not alway clear what a given set of initial data
actually represents. This is especially important for quasiequilibrium data
constructed using the conformal thin-sandwich approach. Most initial-data
studies have focused on identifying data sets that represent binaries in
quasi-circular orbits. In this paper, we consider initial-data sets
representing equal-mass black holes binaries in eccentric orbits. We will show
that effective-potential techniques can be used to calibrate initial data for
black-hole binaries in eccentric orbits. We will also examine several different
approaches, including post-Newtonian diagnostics, for measuring the
eccentricity of an orbit. Finally, we propose the use of the ``Komar-mass
difference'' as a useful, invariant means of parameterizing the eccentricity of
relativistic orbits.Comment: 12 pages, 11 figures, submitted to Physical Review D, revtex
A discrete history of the Lorentzian path integral
In these lecture notes, I describe the motivation behind a recent formulation
of a non-perturbative gravitational path integral for Lorentzian (instead of
the usual Euclidean) space-times, and give a pedagogical introduction to its
main features. At the regularized, discrete level this approach solves the
problems of (i) having a well-defined Wick rotation, (ii) possessing a
coordinate-invariant cutoff, and (iii) leading to_convergent_ sums over
geometries. Although little is known as yet about the existence and nature of
an underlying continuum theory of quantum gravity in four dimensions, there are
already a number of beautiful results in d=2 and d=3 where continuum limits
have been found. They include an explicit example of the inequivalence of the
Euclidean and Lorentzian path integrals, a non-perturbative mechanism for the
cancellation of the conformal factor, and the discovery that causality can act
as an effective regulator of quantum geometry.Comment: 38 pages, 16 figures, typos corrected, some comments and references
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