Relativity Seminar
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Tue, 29/04/2008 12:00 |
Dr. Carsten Gundlach (Southampton) |
Relativity Seminar  |
L3 |
| Current numerical relativity codes model neutron star matter as a perfect fluid, with an unphysical "atmosphere" surrounding the star to avoid the breakdown of the equations at the fluid-vacuum interface at the surface of the star. To design numerical methods that do not require an unphysical atmosphere, it is useful to know what a generic sound wave looks near the surface. After a review of relevant mathematical methods, I will present results for low (finite) amplitude waves that remain smooth and, perhaps, for high amplitude waves that form a shock. | |||
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Tue, 13/05/2008 12:00 |
Michael Holst (University of California, San Diego) |
Relativity Seminar |
L3 |
| > There is currently tremendous interest in geometric PDE, due in part > to the geometric flow program used successfully to attack the Poincare > and Geometrization Conjectures. Geometric PDE also play a primary > role in general relativity, where the (constrained) Einstein evolution > equations describe the propagation of gravitational waves generated by > collisions of massive objects such as black holes.> The need to validate this geometric PDE model of gravity has led to > the recent construction of (very expensive) gravitational wave > detectors, such as the NSF-funded LIGO project. In this lecture, we > consider the non-dynamical subset of the Einstein equations called the > Einstein constraints; this coupled nonlinear elliptic system must be > solved numerically to produce initial data for gravitational wave > simulations, and to enforce the constraints during dynamical > simulations, as needed for LIGO and other gravitational wave modeling efforts.>> The Einstein constraint equations have been studied intensively for > half a century; our focus in this lecture is on a thirty-year-old open > question involving existence of solutions to the constraint equations > on space-like hyper-surfaces with arbitrarily prescribed mean > extrinsic curvature. All known existence results have involved > assuming either constant (CMC) or nearly-constant (near-CMC) mean > extrinsic curvature.> After giving a survey of known CMC and near-CMC results through 2007, > we outline a new topological fixed-point framework that is > fundamentally free of both CMC and near-CMC conditions, resting on the > construction of "global barriers" for the Hamiltonian constraint. We > then present such a barrier construction for case of closed manifolds > with positive Yamabe metrics, giving the first known existence results > for arbitrarily prescribed mean extrinsic curvature. Our results are > developed in the setting of a “weak” background metric, which > requires building up a set of preliminary results on general Sobolev > classes and elliptic operators on manifold with weak metrics. > However, this allows us to recover the recent “rough” CMC existence > results of Choquet-Bruhat> (2004) and of Maxwell (2004-2006) as two distinct limiting cases of > our non-CMC results. Our non-CMC results also extend to other cases > such as compact manifolds with boundary.>> Time permitting, we also outline some new abstract approximation > theory results using the weak solution theory framework for the > constraints; an application of which gives a convergence proof for > adaptive finite element methods applied to the Hamiltonian constraint.This is joint work with Gabriel Nagy and Gantumur Tsogtgerel. | |||
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Tue, 03/06/2008 12:00 |
Gustav Holzegel (Cambridge) |
Relativity Seminar |
L3 |
| I will start by reviewing the current status of the stability problem for black holes in general relativity. In the second part of the talk I will focus on a particular (symmetry) class of five-dimensional dynamical black holes recently introduced by Bizon et al as a model to study gravitational collapse in vacuum. In this context I state a recent result establishing the asymptotic stability of the five dimensional Schwarzschild metric with respect to vacuum perturbations in the given class. | |||
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Tue, 10/06/2008 12:00 |
Prof. R. Meinel (Jena) |
Relativity Seminar |
L3 |
| In this talk I shall review analytical and numerical results on equilibrium configurations of rotating fluid bodies within Einstein's theory of gravitation. | |||
