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On the geometry of pp-wave type spacetimes

José Luis Flores·Miguel Sánchez
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Abstract

Global geometric properties of product manifolds ${\cal M}= M \times \R^2$, endowed with a metric type $<\cdot, \cdot > = < \cdot, \cdot >_R + 2 dudv + H(x,u) du^2$ (where $<\cdot, \cdot >_R$ 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.

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José Luis Flores, Miguel Sánchez. 2004-10-01. On the geometry of pp-wave type spacetimes. https://doi.org/10.1007/11550259_4

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