Related papers: Chronological spacetimes without lightlike lines a…
The result "chronological spacetimes without lightlike lines are stably causal" is announced and motivated. It implies that chronological spacetimes which are null geodesically complete and satisfy the null genericity and the null…
We argue that in the context of string theory, the usual restriction to globally hyperbolic spacetimes should be considerably relaxed. We exhibit an example of a spacetime which only satisfies the causal condition, and so is arbitrarily…
By definition a spacetime is stably causal if it is possible to widen the light cones all over the spacetime without spoiling causality. We prove that if the spacetime is at least non-total imprisoning then it is stably causal provided the…
Reasonable spacetimes are non-compact and of dimension larger than two. We show that these spacetimes are globally hyperbolic if and only if the causal diamonds are compact. That is, there is no need to impose the causality condition, as it…
We show that a globally hyperbolic spacetime containing a trapped surface and satisfying the strong energy condition and a condition on certain radial tidal forces must be timelike geodesically incomplete. This constitutes a "timelike"…
A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a…
No Hopf-Rinow Theorem is possible in Lorentzian Geometry. Nonetheless, we prove that a spacetime is globally hyperbolic if and only if it is metrically complete with respect to the null distance of a time function. Our approach is based on…
We test the chronology protection conjecture in classical general relativity by investigating finitely vicious space-times. First we present singularity theorems in finitely vicious space-times by imposing some restrictions on the…
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. This provides an abstract mathematical setting in which one can study causality independent…
A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a…
It is shown that causally simple inextendible spacetimes are hole-free, thus confirming the expectation that causal simplicity removes holes from spacetime. This result is optimal in the sense that causal simplicity cannot be weakened to…
We show that the solution published in Ref.1 is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, causal symmetry and causal…
The classical definition of {\em global hyperbolicity} for a spacetime $(M,g)$ comprises two conditions: (A) compactness of the diamonds $J^+(p)\cap J^-(q)$, and (B) strong causality. Here we show that condition (B) can be replaced just by…
It is proved that all discontinuity points of a finite cosmological time function, $\tau$, are on past lightlike rays. As a result, it is proved that if $(M,g)$ is a chronological space-time without past lightlike rays then there is a…
We construct stationary flat three-dimensional Lorentzian manifolds with singularities that are obtained from Euclidean surfaces with cone singularities and closed one-forms on these surfaces. In the application to (2+1)-gravity, these…
General relativity does not prohibit the existence of space-times that describe time travel. Consideration of such spaces gives rise to a lot of questions and paradoxes, among which there are thermodynamic ones. This paper considers two…
We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$…
A new concept analogous to global hyperbolicity is introduced, based on test fields. It is shown that the space-times termed here ``curve integrable'' are globally hyperbolic in this new sense, and a plausibility argument is given…
A physical theory of experiments carried out in a space-time region can accommodate a detector localized in another space-like separated region, in three, not necessarily exclusive, ways: 1) the detector formally collapses physical states…
Spacetimes admitting appropriate spatial homothetic Killing vectors are called spatially homothetic spacetimes. Such spacetimes conform to the fact that gravity has no length-scale for matter inhomogeneities. The matter density for such…