# Mathematical Problems of General Relativity I

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*Demetrios Christodoulou*

A publication of the European Mathematical Society

General relativity is a theory proposed by Einstein in 1915 as a
unified theory of space, time and gravitation. It is based on and extends
Newton's theory of gravitation as well as Newton's equations of motion.
It is thus fundamentally rooted in classical mechanics. The theory can
be seen as a development of Riemannian geometry, itself an extension of
Gauss' intrinsic theory of curved surfaces in Euclidean space. The
domain of application of the theory is astronomical systems.

One of the mathematical methods analyzed and exploited in the present
volume is an extension of Noether's fundamental principle connecting
symmetries to conserved quantities. This is involved at a most
elementary level in the very definition of the notion of hyperbolicity
for an Euler-Lagrange system of partial differential equations. Another
method, the study and systematic use of foliations by characteristic
(null) hypersurfaces, is in the spirit of Roger
Penrose's approach in his incompleteness theorem. The methods have applications
beyond general relativity to problems in fluid mechanics and, more
generally, to the mechanics and electrodynamics of continuous media.

The book is intended for advanced students and researchers seeking an
introduction to the methods and applications of general relativity.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in general relativity.