Searcharxiv⌕ Search

arXiv subjects

Bernd Bruegmann

Publications and source records attributed to Bernd Bruegmann.

82 records · Page 5Linked to original sources
arXiv1999

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.

gr-qc↗
arXiv1997

A simple construction of initial data for multiple black holes

We consider the initial data problem for several black holes in vacuum with arbitrary momenta and spins on a three space with punctures. We compactify the internal asymptotically flat regions to obtain a computational domain without inner boundaries. When treated numerically, this leads to a significant simplification over the conventional approach which is based on throats and isometry conditions. In this new setting it is possible to obtain existence and uniqueness of solutions to the Hamiltonian constraint.

gr-qc↗
arXiv1996

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.

gr-qc↗
arXiv1995

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.

gr-qc↗
arXiv1994

On a geometric derivation of Witten's identity for Chern-Simons theory

We present a formal but simple calculational scheme to relate the expectation value of Wilson loops in Chern-Simons theory to the Jones polynomial. We consider the exponential of the generator of homotopy transformations which produces the finite loop deformations that define the crossing change formulas of knot polynomials. Applying this operator to the expectation value of Wilson loops for an unspecified measure we find a set of conditions on the measure and the regularization such that the Jones polynomial is obtained.

hep-th↗
arXiv1992

Non-uniform measure in 4d simplicial quantum gravity

Four-dimensional euclidean quantum gravity has been studied as a discrete model based on dynamical triangulations by Ambjorn and Jurkiewicz and by Agishtein and Migdal. We discuss a particular implementation of a Monte Carlo simulation of simplicial quantum gravity. As an application we introduce a non-uniform measure and examine its effect on simple aspects of the mathematical geometry. We find that the transition region from the hot to the cold phase is shifted and that the criticality of the transition changes.

hep-lat↗
arXiv1992

4d Simplicial Quantum Gravity with a Non-Trivial Measure

We study 4d simplicial quantum gravity in the dynamical triangulation approach with a non-trivial class of measures. We find that the measure contribution plays an important role, influencing the phase diagram and the nature of the (possible) critical theory. We discuss how the lattice theory could be used to fix the quantum measure in a non-ambiguous way.

hep-lat↗
arXiv1992

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.

hep-th↗
arXiv1992

Jones Polynomials for Intersecting Knots as Physical States of Quantum Gravity

We find a consistent formulation of the constraints of Quantum Gravity with a cosmological constant in terms of the Ashtekar new variables in the connection representation, including the existence of a state that is a solution to all the constraints. This state is related to the Chern-Simons form constructed from the Ashtekar connection and has an associated metric in spacetime that is everywhere nondegenerate. We then transform this state to the loop representation and find solutions to all the constraint equations for intersecting loops. These states are given by suitable generalizations of the Jones knot polynomial for the case of intersecting knots. These are the first physical states of Quantum Gravity for which an explicit form is known both in the connection and loop representations. Implications of this result are also discussed.

hep-th↗