Geodesic connectedness and conjugate points in GRW spacetimes

Abstract

Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesic connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional spacetimes and to GRW spacetimes satisfying the timelike convergence condition are also found.

31 pages and 2 figures

References in corpus (4)

• A Morse Theory for Massive Particles and Photons in General Relativity
• How to measure spatial distances?
• A Generalized Index Theorem for Morse-Sturm Systems and Applications to semi-Riemannian Geometry
• Convexity of domains of Riemannian manifolds

Cited by in corpus (7)

• Curvature of Multiply Warped Products
• $2-$Killing Vector Fields on Warped Product Manifolds
• Induced Riemannian structures on null hypersurfaces
• On symmetries of generalized Robertson-Walker Space-times and applications
• Concircular curvature on warped product manifolds and applications
• Totally umbilic null hypersurfaces in generalized Robertson-Walker spaces
• On causality and closed geodesics of compact Lorentzian manifolds and static spacetimes