Existence of closed timelike geodesics in Lorentz spaces

@inproceedings{Tipler1979ExistenceOC,
  title={Existence of closed timelike geodesics in Lorentz spaces},
  author={Frank Tipler},
  year={1979}
}
Certain classes of compact four-dimensional Lorentz spaces are shown to possess at least one closed timelike geodesic. 
Timelike periodic trajectories in spatially compact Lorentz manifolds
A result on the existence of timelike periodic trajectories in a general class of Lorentzian manifolds R x M, with compact M, is obtained. The proof is based on arguments concerning closed geodesics
A new class of compact spacetimes without closed causal geodesics
We construct the first examples of geodesically complete compact spacetimes admitting a regular globally hyperbolic covering, but which do not contain closed causal geodesics.
Periodic Geodesics and Geometry of Compact Stationary Lorentzian Manifolds
We prove the existence of at least two timelike non self-int ersecting periodic geodesics in compact stationary Lorentzian manifolds and w e discuss some properties of the topology of such manifolds.
GEODESICS IN LORENTZIAN SURFACES
We show that every closed Lorentzian surface contains at least two closed geodesics. Explicit examples show the optimality of this claim. Refining this result we relate the least number of closed
Some global properties of static spacetimes
Abstract. We show that a static Lorentzian manifold satisfying a completeness assumption is geodesically connected. In particular, such condition is satisfied by all compact static manifolds; in the
On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes
Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct
Compact flat spacetimes
Lorentzian covering space and homotopy classes
We analyze structures of covering space over a Lorentzian manifold. By use of this we show that, if a Lorentzian manifold is globally hyperbolic then for any two causally related points p and q, the
...
...

References

SHOWING 1-6 OF 6 REFERENCES
Techniques of Differential Topology in Relativity
Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.
Topology in general relativity
A number of theorems and definitions which are useful in the global analysis of relativistic world models are presented. It is shown in particular that, under certain conditions, changes in the
Lectures on closed geodesics
1. The Hilbert Manifold of Closed Curves.- 1.1 Hilbert Manifolds.- 1.2 The Manifold of Closed Curves.- 1.3 Riemannian Metric and Energy Integral of the Manifold of Closed Curves.- 1.4 The Condition
The domain of dependence
The various properties of the domain of dependence (Cauchy development) which have been found particularly useful in the study of gravitational fields are reviewed. The basic techniques for
The Large Scale Structure of Space-Time
TLDR
The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.
Geroch, Topology in general relativity
  • J. Mathematical Phys
  • 1967