Mathematical general relativity: a sampler
arXiv:1004.1016
Abstract
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
Some updates. A shortened version, to appear in the Bulletin of the AMS, is available online at http://www.ams.org/journals/bull/0000-000-00/S0273-0979-2010-01304-5
References in corpus (35)
- A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
- Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
- Black ring with two angular momenta
- A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta
- On the uniqueness of smooth, stationary black holes in vacuum
- Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime
- Extremality conditions for isolated and dynamical horizons
- A Uniqueness theorem for 5-dimensional Einstein-Maxwell black holes
- Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum
- The time evolution of marginally trapped surfaces
- Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass
- Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics
- Uniqueness results for ill posed characteristic problems in curved space-times
- Construction of N-body initial data sets in general relativity
- All Vacuum Near-Horizon Geometries in -dimensions with Commuting Rotational Symmetries
- A model problem for conformal parameterizations of the Einstein constraint equations
- Generalized inverse mean curvature flows in spacetime
- Gluing Initial Data Sets for General Relativity
- Aperiodic oscillatory asymptotic behavior for some Bianchi spacetimes
- On characteristic initial data for a star orbiting a black hole
- Linear Waves in the Kerr Geometry: A Mathematical Voyage to Black Hole Physics
- The light-cone theorem
- The BKL Conjectures for Spatially Homogeneous Spacetimes
- The Formation of Black Holes in General Relativity
- Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity
- Phase space for the Einstein equations
- Rough Solutions of the Einstein Constraint Equations
- Conformal boundary extensions of Lorentzian manifolds
- Global characteristic problem for the Einstein vacuum equations with small initial data, (II): The existence proof
- On the global structure of the Pomeransky-Senkov black holes
- Hawking's local rigidity theorem without analyticity
- Singular Yamabe metrics and initial data with exactly Kottler-Schwarzschild-de Sitter ends II. Generic metrics
- Decay of the Maxwell field on the Schwarzschild manifold
- Applications of theorems of Jean Leray to the Einstein-scalar field equations
- The power of monitoring stellar orbits