Global problems in mathematical relativity

Programme theme

General relativity has been around for a long time as a physical theory and an object of mathematical study. It was a subject of intense interest in the 1960s and 1970s when advances included the discovery of the Kerr solution, the study of black holes and singularity theorems and the introduction of asymptopia as a framework for studying asymptotic properties, including gravitational radiation. At the same time there were many mathematical problems which resisted mathematical analysis. In recent years there have been significant advances in our understanding of the topological, geometrical and PDE aspects of general relativity and progress is once again becoming rapid. New results are being obtained, and older results re-proved in greater generality.

This programme will be structured around four themes:

Elliptic aspects of general relativity: new methods of solving the constraint equations, developments from the solution of the Riemannian Penrose inequality, the study of static and stationary solutions including black holes.
Hyperbolic aspects of general relativity: local and global evolution problems, Cosmic Censorship conjecture, and the nature of singularities.
Global Lorentzian geometry: global techniques and asymptotic structure, splitting theorems and extendibility.
New methods in general relativity: inverse scattering and boundary-value problems, scattering theory for linear field equations, new methods from Riemannian geometry.

While all four themes will be worked on throughout the programme, and indeed it would be neither possible nor desirable to keep them rigidly separate, there will be periods of more focus on each. The overall emphasis will be on mathematical results and global properties of solutions of the Einstein equations, but it is worth noting that there is a clear motivation from physics to deepen our understanding of general relativity, at a time when gravitational wave detectors around the world have started collecting data.

Thematic Diary

8 - 21 August: Hyperbolic problems (organised by I Rodnianski and H Friedrich)
15 - 21 August: Numerical relativity (organised by L Lehner and H Friedrich, including a Satellite Meeting in Southampton organised by C Gundlach and H Friedrich)
21 - 27 August: Euroconference - Global general relativity
30 August - 11 September: Black holes (organised by R Wald and PT Chrusciel)
12 - 25 September: Dynamical systems (organised by A Rendall and H Ringström and P Tod)
26 September - 9 October: Riemannian geometry and GR (organised by M Anderson and PT Chrusciel)
10 - 16 October: Lorentzian geometry (organised by A Zeghib and PT Chrusciel)
17 - 23 October: Global techniques (organised by G Galloway and PT Chrusciel)
17 October - 13 November: Quantum aspects (organised by A Ashtekar and PT Chrusciel)
14 - 20 November: Asymptotic structure
21 - 27 November: Inverse scattering and integrability (organised by G Neugebauer and P Tod)
28 November - 11 December: Static/stationary solutions (organised by R Beig and PT Chrusciel)
5 - 23 December: Constraint equations (organised by J Isenberg and PT Chrusciel)
12 - 16 December: Einstein Constraint Equations (organised by J Isenberg and PT Chrusciel)

This structure is intended to indicate at which period somebody who is interested in a particular subject is more likely to meet people interested in the same subject.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme
Inextendibility of expanding cosmological models with symmetry Authors: Alan Rendall, M Dafermos Download PDF	2005	GMR	21 October 2016
A generalization of Hawking's black hole topology theorem to higher dimensions Authors: R Schoen, G Galloway Download PDF	2005	GMR	21 October 2016
On the nonlinear stability of higher-dimensional triaxial Bianchi IX black holes Authors: G Holzegel, M Dafermos Download PDF	2005	GMR	21 October 2016
A gradient flow for worldsheet nonlinear sigma models Authors: V Suneeta, T Oliynyk, Eric Woolgar Download PDF	2005	GMR	21 October 2016
Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations Authors: C Bona, L Lehner, C Palenzuela-Luque Download PDF	2005	GMR	21 October 2016
AMR, stability and higher accuracy Authors: SL Liebling, O Reula, L Lehner Download PDF	2005	GMR	21 October 2016
The index form of a warped product Authors: SB Kim, PE Ehrlich Download PDF	2005	GMR	21 October 2016
Killing vectors in asymptotically flat space-times: II. asymptotically translational killing vectors and the rigid positive energy theorem in higher dimensions Authors: Daniel Maerten, Piotr Chrusciel Download PDF	2005	GMR	21 October 2016
Effective equations of motion for quantum systems Authors: A Skirzewski, Martin Bojowald Download PDF	2005	GMR	21 October 2016
Perturbative degrees of freedom in loop quantum gravity: anisotrophies Authors: HH Hernandez, HM Tecotl, Martin Bojowald Download PDF	2005	GMR	21 October 2016
Spherically symmetric quantum geometry: Hamiltonian constraint Authors: R Swiderski, Martin Bojowald Download PDF	2005	GMR	21 October 2016
On non-existence of static vacuum black holes with degenerate components of the event horizon Authors: HS Reall, P Tod, Piotr Chrusciel Download PDF	2005	GMR	21 October 2016
The classification of static electro-vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior Authors: P Tod, Piotr Chrusciel Download PDF	2005	GMR	21 October 2016
On vacuum gravitational collapse in nine dimensions Authors: P Bizon, T Chmaj, A Rostworowski, ET Al Download PDF	2005	GMR	21 October 2016
The Cauchy problem for Schrodinger flows into Kahler manifolds Authors: D Pollack, G Staffilani, ET Al, C Kenig Download PDF	2005	GMR	21 October 2016
On the black hole limit of rotating fluid bodies in equilibrium Authors: Reinhard Meinel Download PDF	2005	GMR	21 October 2016
Timelike minimal submanifolds of general co-dimension in Minkowski spacetime Authors: L Andersson, J Isenberg, P Allen Download PDF	2005	GMR	21 October 2016
Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations Authors: C Uggla, Mark Heinzle Download PDF	2005	GMR	21 October 2016
On the motion of a compact elastic body Authors: Robert Beig, Michael Wernig-Pichler Download PDF	2005	GMR	21 October 2016
Spherically symmetric dynamical horizons Authors: J Isenberg, R Bartnik Download PDF	2005	GMR	21 October 2016
A note on static metrics Authors: P Tod, R Bartnik Download PDF	2005	GMR	21 October 2016
The Ernst equation and ergosurfaces Authors: Piotr Chrusciel, Reinhard Meinel, Sebastian Szybka Download PDF	2005	GMR	21 October 2016
An integral equation for spacetime curvature in general relativity Authors: V Moncrief Download PDF	2005	GMR	21 October 2016
Analytic reductions of self-force calculations in curved spacetimes Authors: V Moncrief Download PDF	2005	GMR	21 October 2016
On existence of non-singular, vacuum, stationary space-times with a negative cosmological constant Authors: Erwann Delay, Piotr Chrusciel Download PDF	2005	GMR	21 October 2016
On Israel-Wilson-Perjes black holes Authors: HS Reall, P Tod, Piotr Chrusciel Download PDF	2005	GMR	21 October 2016
Anti-self-dual conformal structures with null Killing vectors from projective structures Authors: S West, M Dunajski Download PDF	2005	GMR	21 October 2016
Einstein-Maxwell-Dilaton metrics from three-dimensional Einstein-Weyl structures Authors: M Dunajski Download PDF	2005	GMR	21 October 2016
On a class of 2-surface observables in general relativity Authors: LB Szabados Download PDF	2005	GMR	21 October 2016
Curvature estimates for stable marginally trapped surfaces Authors: Jan Metzger, L Andersson Download PDF	2005	GMR	21 October 2016
Quantum energy inequalities and local covariance I: Globally hyperbolic spacetimes Authors: MJ Pfenning, CJ Fewster Download PDF	2005	GMR	21 October 2016
Motion of isolated bodies Authors: Yvonne Choquet-Bruhat, H Friedrich Download PDF	2005	GMR	21 October 2016
Static vacuum solutions from convergent null data expansions at space-like infinity Authors: H Friedrich Download PDF	2005	GMR	21 October 2016
How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile Authors: A Satz, J Louko Download PDF	2005	GMR	21 October 2016
Excited by a quantum field: Does shape matter? Authors: A Satz, J Louko Download PDF	2005	GMR	21 October 2016
The asymptotics of stationary electro-vacuum metrics in odd space-time dimensions Authors: Robert Beig, Piotr Chrusciel Download PDF	2005	GMR	21 October 2016
Strong cosmic censorship for ${\it T}^2$ -symmetric cosmological spacetimes with collisionless matter Authors: M Dafermos, Alan Rendall Download PDF	2005	GMR	21 October 2016
Anti-self-dual conformal structures in neutral signature Authors: S West, M Dunajski Download PDF	2005	GMR	21 October 2016
Quantum gravity and the Coulomb potential Authors: J Louko, O Winkler, V Husain Download PDF	2005	GMR	21 October 2016

Workshops

GMRW01

Seminars

Tuesday 9th August 2005
10:30 to 11:30	Gowdy Cosmologies: Theorems and Simulations Working Together	Room 2

Thursday 11th August 2005
10:30 to 12:00	The Bianchi system	Room 2

Monday 15th August 2005
15:30 to 17:00	Numerical analysis and numerical relativity	Room 1

Tuesday 16th August 2005
10:30 to 11:30	Lars Andersson On the interaction of mathematical and numerical general relativity	Room 2

Wednesday 17th August 2005
10:30 to 12:00	Hyperbolicity of second order in space systems of evolution equations	Room 1

Tuesday 30th August 2005
15:30 to 16:30	Hubert Bray Duke University Negative point mass singularities in general relativity	Room 1

Wednesday 31st August 2005
15:30 to 16:30	Geons with spin and charge	Room 1

Monday 5th September 2005
14:00 to 15:00	Self-similar gravitational collapse and gravitational instantons	Room 1
15:30 to 16:30	On stability of higher dimensional static black holes	Room 1

Tuesday 6th September 2005
15:30 to 16:30	Jean-Philippe Nicolas Université Bordeaux 1 Conformal scattering and the Goursat problem, main ideas and what perspectives for black hole space-times?	Room 1

Wednesday 7th September 2005
15:30 to 16:30	Stability of marginally trapped surfaces and local existence of dynamical and trapping horizons	Room 1

Monday 12th September 2005
16:00 to 17:00	Vacuum gravitational collapse in 4+1 dimensions	Room 1

Tuesday 13th September 2005
16:00 to 17:00	Dynamics of Bianchi space-times	Room 1

Thursday 15th September 2005
16:00 to 17:00	Mark Heinzle Asymptotic expansions and nonlinear stability of power-law inflation models	Room 1

Monday 19th September 2005
16:00 to 17:00	Accelerated expanding models with Vlasov matter	Room 1

Tuesday 20th September 2005
16:00 to 17:00	Sophonie Blaise Tchapnda The surface-symmetric Einstein-Vlasov system with positive cosmological constant	Room 1

Thursday 22nd September 2005
16:00 to 17:00	Global classical solutions to the 3D Nordstrom-Vlasov system	Room 1

Tuesday 27th September 2005
16:00 to 17:00	Killing spinors, from general relativity to supergravity	Room 2

Wednesday 28th September 2005
16:00 to 17:00	Marc Herzlich Eigenvalue extremality for the Dirac operator on the sphere	Room 2

Thursday 29th September 2005
16:00 to 17:00	On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds	Room 2

Friday 30th September 2005
16:00 to 17:00	Conserved quantities and rigidity for locally AdS spaces	Room 2

Tuesday 4th October 2005
16:00 to 17:00	Eric Woolgar University of Alberta A gradient flow for the nonlinear sigma model at 1-loop: the physics of Perelman's entropy	Room 1

Thursday 6th October 2005
16:00 to 17:00	Einstein metrics on product spaces	Room 1

Friday 7th October 2005
16:00 to 17:00	Sectional curvature and general relativity	Room 1

Monday 10th October 2005
16:00 to 17:00	Complete Flat Lorentzian 3-Manifolds	Room 1

Tuesday 11th October 2005
16:00 to 17:00	Barriers and CMC hypersurfaces	Room 1

Thursday 13th October 2005
16:00 to 17:00	Abdelghani Zeghib On CMC foliations	Room 1

Monday 17th October 2005
16:00 to 17:00	Second variation in general relativity	Room 1

Tuesday 18th October 2005
16:00 to 17:00	Mathematical introduction to loop quantum gravity	Room 1

Wednesday 19th October 2005
11:00 to 12:30	Introduction to algebraic quantum field theory in curved spacetime	Room 2
16:00 to 17:00	Comparison theory in Lorentzian geometry	Room 1

Thursday 20th October 2005
16:00 to 17:00	Martin Bojowald Loop quantum cosmology	Room 1

Friday 21st October 2005
11:00 to 12:30	Energy conditions in quantum field theory	Room 2
16:00 to 17:00	Francesco Nicolo A global solution for a characteristic problem for the Einstein vacuum equations with small initial data	Room 1

Monday 24th October 2005
11:00 to 12:30	Discussions on recent developments in mathematical quantum gravity	Room 2

Tuesday 25th October 2005
15:30 to 16:30	Hanno Sahlmann Uniqueness of the kinematical representation of loop quantum gravity	Room 1

Wednesday 26th October 2005
11:00 to 12:30	Discussions on recent developments in mathematical quantum gravity	Room 2

Thursday 27th October 2005
16:00 to 17:00	Quantum geometry and space-time singularities	Room 1

Friday 28th October 2005
11:00 to 12:30	Radiation-reaction on timelike surfaces in AdS	Room 2

Tuesday 1st November 2005
16:00 to 17:00	Constrained systems: Dirac and post-Dirac quantisation	Room 1

Wednesday 2nd November 2005
11:00 to 12:30	The Hamiltonian constraint in loop quantum gravity	Room 2

Thursday 3rd November 2005
16:00 to 17:00	Colombeau algebras in GR	Room 1

Friday 4th November 2005
11:00 to 12:30	The master constraint programme for loop quantum gravity	Room 2

Tuesday 8th November 2005
16:00 to 17:00	Spin foam quantum gravity	Room 1

Wednesday 9th November 2005
11:00 to 12:30	The representation ambiguity in loop quantum gravity	Room 2

Thursday 10th November 2005
16:00 to 17:00	Carlo Rovelli Definition of n-point function in nonperturbative quantum gravity and low energy limit of the loop-spin foam formalism	Room 1

Friday 11th November 2005
11:00 to 12:30	Carlo Rovelli Discussions on n-point functions in non-perturbative quantum gravity	Room 2

Monday 14th November 2005
16:00 to 17:00	Juan Antonio Valiente Kroon Birkbeck, University of London Time asymmetric spacetimes near null and spatial infinity	Room 1

Tuesday 15th November 2005
16:00 to 17:00	Asymptotically AdS-spacetimes	Room 1

Wednesday 16th November 2005
16:00 to 17:00	Decay and the conformal energy of waves around the Schwarzschild black hole	Room 1

Thursday 17th November 2005
16:00 to 17:00	Asymptotic flatness at null infinity in higher dimensional gravity	Room 1

Friday 18th November 2005
16:00 to 17:00	A new development of the causal boundary of spacetimes	Room 1

Monday 28th November 2005
16:00 to 17:00	Robert Beig On the motion of a compact elastic body	Room 1

Tuesday 29th November 2005
14:30 to 15:30	Mark Heinzle Static perfect fluid models - a dynamical systems approach	Room 1
16:00 to 17:00	David Petroff The extreme distortion of black holes due to matter	Room 1

Thursday 1st December 2005
16:00 to 17:00	The abundant richness of Einstein-Yang-Mills	Room 1

Friday 2nd December 2005
16:00 to 17:00	On the convergence of certain expansions at space-like infinity of asymptotically flat, static vacuum solutions	Room 1

Tuesday 6th December 2005
16:00 to 16:30	Piotr Chrusciel The classification of static electrovacuum black holes	Room 1
16:30 to 17:00	Spherically symmetric dynamical horizons	Room 1

Thursday 8th December 2005
16:00 to 17:00	Second order perturbations of rotating bodies in equilibrium; the exterior vacuum problem	Room 1

Friday 9th December 2005
11:00 to 12:00	QL Mass definitions with positivity proofs	Room 1
16:00 to 17:00	Nonlinear Approximation Techniques in General Relativity and Geometric Analysis	Room 1

Global problems in mathematical relativity

Organisers

Piotr Chrusciel
Helmut Friedrich
Paul Tod University of Oxford

Speakers

Lars Andersson
Robert Beig
Martin Bojowald
Hubert Bray Duke University
Piotr Chrusciel
Mark Heinzle
Marc Herzlich
Jean-Philippe Nicolas Université Bordeaux 1
Francesco Nicolo
David Petroff
Carlo Rovelli
Hanno Sahlmann
Sophonie Blaise Tchapnda
Juan Antonio Valiente Kroon Birkbeck, University of London
Eric Woolgar University of Alberta
Abdelghani Zeghib

Show All

Global problems in mathematical relativity

Programme theme

Thematic Diary

Preprints

Inextendibility of expanding cosmological models with symmetry

A generalization of Hawking's black hole topology theorem to higher dimensions

On the nonlinear stability of higher-dimensional triaxial Bianchi IX black holes

A gradient flow for worldsheet nonlinear sigma models

Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations

AMR, stability and higher accuracy

The index form of a warped product

Killing vectors in asymptotically flat space-times: II. asymptotically translational killing vectors and the rigid positive energy theorem in higher dimensions

Effective equations of motion for quantum systems

Perturbative degrees of freedom in loop quantum gravity: anisotrophies

Spherically symmetric quantum geometry: Hamiltonian constraint

On non-existence of static vacuum black holes with degenerate components of the event horizon

The classification of static electro-vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior

On vacuum gravitational collapse in nine dimensions

The Cauchy problem for Schrodinger flows into Kahler manifolds

On the black hole limit of rotating fluid bodies in equilibrium

Timelike minimal submanifolds of general co-dimension in Minkowski spacetime

Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations

On the motion of a compact elastic body

Spherically symmetric dynamical horizons

A note on static metrics

The Ernst equation and ergosurfaces

An integral equation for spacetime curvature in general relativity

Analytic reductions of self-force calculations in curved spacetimes

On existence of non-singular, vacuum, stationary space-times with a negative cosmological constant

On Israel-Wilson-Perjes black holes

Anti-self-dual conformal structures with null Killing vectors from projective structures

Einstein-Maxwell-Dilaton metrics from three-dimensional Einstein-Weyl structures

On a class of 2-surface observables in general relativity

Curvature estimates for stable marginally trapped surfaces

Quantum energy inequalities and local covariance I: Globally hyperbolic spacetimes

Motion of isolated bodies

Static vacuum solutions from convergent null data expansions at space-like infinity

How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile

Excited by a quantum field: Does shape matter?

The asymptotics of stationary electro-vacuum metrics in odd space-time dimensions

Strong cosmic censorship for ${\it T}^2$ -symmetric cosmological spacetimes with collisionless matter

Anti-self-dual conformal structures in neutral signature

Quantum gravity and the Coulomb potential

Workshops

Seminars

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Speakers

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