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Analytical and Numerical Approaches to Mathematical Relativity, p. 79-98, 2006

DOI: 10.1007/11550259_4

Analytical and Numerical Approaches to Mathematical Relativity, p. 79-98

DOI: 10.1007/3-540-33484-x_4

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On the geometry of pp-wave type spacetimes

Journal article published in 1970 by José Luis Flores, Miguel Sánchez ORCID
This paper is available in a repository.
This paper is available in a repository.

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Abstract

Global geometric properties of product manifolds ${\cal M}= M \times \R^2$, endowed with a metric type $ = _R + 2 dudv + H(x,u) du^2$ (where $_R$ is a Riemannian metric on $M$ and $H:M \times \R \to \R$ a function), which generalize classical plane waves, are revisited. Our study covers causality (causal ladder, inexistence of horizons), geodesic completeness, geodesic connectedness and existence of conjugate points. Appropiate mathematical tools for each problem are emphasized and the necessity to improve several Riemannian (positive definite) results is claimed. ; Comment: 19 pages, Proceedings of the March-2004 Heraeus Seminar "Mathematical Relativity: New ideas and developments"