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On the Geometry of pp-Wave Type Spacetimes

  • José L. Flores
  • Miguel Sánchez
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 692)

Abstract

Global geometric properties of product manifolds M = M × ℝ2, endowed with a metric type 〈·,·〉 = 〈·,·〉 R + 2dudv + H(x,u)du 2 (where 〈·,·〉 R is a Riemannian metric on M and H : M×ℝ → ℝ a function), which generalize classical plane waves, are revisited. Our study covers causality (causal ladder, non-existence of horizons), geodesic completeness, geodesic connectedness and existence of conjugate points. Appropriate mathematical tools for each problem are emphasized and the necessity to improve several Riemannian (positive de.nite) results is claimed.

Keywords

Plane Wave Gravitational Wave Riemannian Problem Conjugate Point Geodesic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2006

Authors and Affiliations

  • José L. Flores
    • 1
    • 2
  • Miguel Sánchez
    • 3
  1. 1.Department of MathematicsStony Brook University, Stony BrookUSA
  2. 2.Departamento de Álgebra, Geometría y TopologíaUniversidad de Málaga, Campus TeatinosMálagaSpain
  3. 3.Departamento de Geometría y TopologíaFacultad de Ciencias, Universidad de GranadaGranadaSpain

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