By Paul E. Ehrlich (auth.), Jörg Frauendiener, Domenico J.W. Giulini, Volker Perlick (eds.)

ISBN-10: 3540310274

ISBN-13: 9783540310273

Today, basic relativity charges one of the such a lot correctly validated primary theories in all of physics. even though, deficiencies in our mathematical and conceptual figuring out nonetheless exist, and those in part impede extra growth. as a result by myself, yet no less significant from the viewpoint theory-based prediction will be considered as no larger than one's personal structural figuring out of the underlying conception, one may still adopt severe investigations into the corresponding mathematical matters. This ebook features a consultant number of surveys by way of specialists in mathematical relativity writing concerning the present prestige of, and difficulties in, their fields. There are 4 contributions for every of the subsequent mathematical parts: differential geometry and differential topology, analytical equipment and differential equations, and numerical equipment. This booklet addresses graduate scholars and expert researchers alike.

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J. Cheeger, D. Ebin: Comparison Theorems in Riemannian Geometry (North– Holland, Amsterdam 1975) 21 28. J. Cheeger, D. Gromoll: The splitting theorem for manifolds of nonnegative Ricci curvature. J. Diﬀ. Geom. 6, 119–128 (1971) 17, 18 29. S. Clarke: On the geodesic completeness of causal space-times. Proc. Camb. Phil. Soc. 69, 319–324 (1971) 8 30. P. Eberlein, B. O’Neill: Visibility manifolds. Paciﬁc J. Math. 46, 45–109 (1973) 5, 30 31. E. Ehrlich: Metric deformation of curvature. I: Local convex deformations.

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H. Eschenburg: The splitting theorem for space-times with strong energy condition. J. Diﬀ. Geom. 27, 477–491 (1988) 20 38. -H. Eschenburg, E. Heintze: An elementary proof of the Cheeger–Gromoll splitting theorem, Ann. Global Analysis Geometry 2, 141–151 (1984) 18 39. L. Flores, M. S´ anchez: Causality and conjugate points in general plane waves. Class. Quantum Grav. 20, 2275–2291 (2003) 30 40. T. H. Freeman, San Francisco 1979) 23 41. G. Galloway: Splitting theorems for spatially closed space-times.

### Analytical and Numerical Approaches to Mathematical Relativity by Paul E. Ehrlich (auth.), Jörg Frauendiener, Domenico J.W. Giulini, Volker Perlick (eds.)

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