Atomization Theorems in Mathematical Physics and General Relativity

Mathematical General Relativity: a Sampler

We provide an introduction to selected significant advances in the mathematical understanding of Einstein’s theory of gravitation which have taken place in recent years.

Institute for Mathematical Physics Asymptotic Structure of Symmetry Reduced General Relativity Asymptotic Structure of Symmetry Reduced General Relativity

Gravitational waves with a space-translation Killing eld are considered. In this case, the 4-dimensional Einstein vacuum equations are equivalent to the 3-dimensional Einstein equations with certain matter sources. This interplay between 4-and 3-dimensional general relativity can be exploited eeectively to analyze issues pertaining to 4 dimensions in terms of the 3-dimensional structures. An ex...

Recent Mathematical Developments in Quantum General Relativity

After a brief chronological sketch of developments in non-perturbative canonical quantum gravity, some of the recent mathematical results are reviewed. These include: i) an explicit construction of the quantum counterpart of Wheeler’s superspace; ii) a rigorous procedure leading to the general solution of the diffeomorphism constraint in quantum geometrodynamics as well as connection dynamics; ...

Institute for Mathematical Physics Stable Singularities of Wave Fronts in General Relativity

Some Remarks on Mathematical General Relativity Theory

This paper gives a brief survey of the development of general relativity theory starting from Newtonian theory and Euclidean geometry and proceeding through to special relativity and finally to general relativity and relativistic cosmology.