Mehdi Vatandoost | Searcharxiv

arXiv2021

Causally simple spacetimes and naked singularities

In this paper, We prove a conjecture which states that if M is a nakedly singular future boundary or nakedly singular past boundary spacetime, then the space of null geodesics, N, is non-Hausdorff. Also, we show that every two-dimensional strongly causal spacetime M is causally simple if and only if it is null pseudoconvex. As a result, it implies the converse of the conjecture for two-dimension but there are examples that refute it for more dimensions.

gr-qc↗

arXiv2020

The cosmological time functions and lightlike rays

It is proved that all discontinuity points of a finite cosmological time function, $τ$, 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 representation of $g$ such that its cosmological time function is regular. In addition, by reducing conditions of regularity sufficient conditions for causal simplicity and causal pseudoconvexity of space-time is given. It is also proved that the second condition of regularity can be reduced to satisfies only on inextendible past-directed causal rays if $(M,g)$ be a space-time, conformal with an open subspace of Minkowski space-time or $τ$ be continuous.

gr-qc↗