3.6 General Relativity

Organizers P. Chrusciel (Tours), H. Nicolai (Golm)

3.6.1 Einstein Spaces as Attractors for the Einstein Flow

Lars Andersson

Albert Einstein Institut, Golm laan@aei.mpg.de

I will discuss a proof of nonlinear stability of Lorentz cones over Riemannian negative Einstein spaces M of arbitrary dimension, generalizing earlier work in the 3 + 1 dimensional case. In the higher dimensional case several new phenomena arise. The asymptotic rate of decay depends on the spectral properties of the background geometry. Further, there may be a nontrivial deformation space of negative Einstein spaces on M, examples are provided by Kähler-Einstein spaces. In spacetime dimensions greater than 10, our work allows one to construct large families of vacuum spacetimes with quiescent singularity and asymptotically Friedman behavior in the expanding direction. This talk is based on joint work with Vince Moncrief.

3.6.2 Loop Quantum Cosmology

Martin Bojowald

Penn State Univ. bojowald@gravity.psu.edu

Focussing on mathematical aspects, this talk will give a review of loop quantum cosmology, which is an application of background independent quantization techniques to cosmological models. Due to discrete spatial geometry as a consequence of the quantization, dynamical equations in such models are difference rather than differential equations. Suitable solutions display typical features in quantum regimes, where they can resolve classical space-time singularities, but should also approach semiclassical behavior in classical regimes. Such solutions can be found using generating function or continued fraction techniques. Semiclassical behavior and corrections to the classical one are derived using effective equations which approximate partial difference equations by ordinary differential equations.

3.6.3 The Red-Shift Effect and Radiation Decay on Black Hole Space-Times

Mihaelis Dafermos

Cambridge

M.Dafermos@dpmms.cam.ac.uk

I will present proofs of uniform decay rates for solutions to the wave equation on various black hole exterior backgrounds. This is joint work with I. Rodnianski.

3.6.4 Angular Momentum-Mass Inequality for Axisymmetric Black Holes

Sergio Dain

Univ. de Cordoba

dain@famaf.unc.edu.ar

√

In this talk I will discuss the physical relevance of the inequality J ≤ m, where m and J are the total mass and angular momentum, for axially symmetric (nonstationary) black holes. In particular, I will prove that for vacuum, maximal, complete, asymptotically flat, axisymmetric initial data, this inequality is satisfied. The proof consists in showing that extreme Kerr is a global minimum of the mass.

3.6.5 Black Hole Entropy in Supergravity and String Theory

Gabriel Cardoso

Universität München gcardoso@theorie.physik.uni-muenchen.de

We review recent results on subleading corrections to the entropy of extremal black holes in supergravity and string theory.

3.6.6 Infinite-Dimensional R-Symmetry in Supergravity

Axel Kleinschmidt

Universtät Oldenburg axel.kleinschmidt@aei.mpg.de

Recent work devoted to the study of symmetry structures of supergravity, or the unifying M-theory, has revealed interesting links to the theory of Kac-Moody algebras and their subalgebras. After reviewing these links for the bosonic fields of the theory I will discuss how the fermionic fields fit into the picture. This requires non-trivial results on the mathematical structure of some infinite-dimensional algebras which go beyond the Kac-Moody class. These results permit one to find a common origin of all fermionic fields appearing in the various maximal supergravity theories.