Ja n 20 02 Geodesic connectedness and conjugate points in GRW spacetimes
نویسندگان
چکیده
Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesics 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. ∗Research partially supported by a MEC grant number PB97-0784-C03-01.
منابع مشابه
Geodesic connectedness and conjugate points in GRW space–times
Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesics 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 conditi...
متن کاملGeodesic connectedness of multiwarped spacetimes
A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer’s topological degree for the solution of functional equations. It is shown to be very useful for multiwarped spacetimes, which include different types of relativistic spacetimes. Connectedness by causal geodesics is also proved. r 2002 Elsevier Science (U...
متن کاملOn the Geometry of PP-Wave Type Spacetimes
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, inexistence of horizons), geodesic completeness, geodesic connectedness and existence of conjugate...
متن کاملGeodesic Connectedness of Semi-riemannian Manifolds
The problem of geodesic connectedness in semi-Riemannian manifolds (i.e. the question whether each two points of the manifold can be joined by a geodesic) has been widely studied from very different viewpoints. Our purpose is to review these semi-Riemannian techniques, and possible extensions. In the Riemannian case, it is natural to state this problem on (incomplete) manifolds with (possibly n...
متن کاملr - qc / 0 20 10 45 v 1 1 4 Ja n 20 02 Axial symmetry and conformal Killing vectors
Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in con-formally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, ...
متن کامل