Related papers: Causally simple spacetimes and naked singularities

We show that when a spacetime $\mathcal{M}(=M \cup \partial M)$ is globally hyperbolic with (possibly empty) smooth timelike boundary $\partial M$, a metrizable topology, the closed limit topology (CLT) introduced by F. Hausdorff himself in…

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space-time and appearance of naked singularity has been analyzed both for non-marginal and marginally bound cases. It has been shown that naked…

Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well…

We use techniques based on the splitting tensor to explicitly integrate the Codazzi equation along the relative nullity distribution and express the second fundamental form in terms of the Jacobi tensor of the ambient space. This approach…

This work is essentially a review of a new spacetime model with closed causal curves, recently presented in another paper (Class. Quantum Grav. \textbf{35}(16) (2018), 165003). The spacetime at issue is topologically trivial, free of…

In this article, we extend a construction of [6] to obtain a large class of vacuum cosmological spacetimes that do not contain any CMC Cauchy surfaces. The allowed spatial topologies for these examples are of the form $M \# M$, where $M$ is…

We consider spacetimes with compact Cauchy hypersurfaces and with Ricci tensor bounded from below on the set of timelike unit vectors, and prove that the results known for spacetimes satisfying the timelike convergence condition, namely,…

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…

A topological space $X$ is strongly $D$ if for any neighbourhood assignment $\{U_x:x\in X\}$, there is a $D\subseteq X$ such that $\{U_x:x\in D\}$ covers $X$ and $D$ is locally finite in the topology generated by $\{U_x:x\in X\}$. We prove…

The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes…

We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic…

The Janis-Newman-Winicour (JNW) spacetime possesses a naked singularity, although it represents an exact particle-like solution to the Einstein-Klein-Gordon theory with a massless scalar field. Here, we investigate the possible formation of…

We consider the duality between General Relativity and the theory of Einstein algebras, in the extended setting where one permits non-Hausdorff manifolds. We show that the duality breaks down, and then go on to discuss a sense in which…

The order horismos induces the Zeeman $Z$ topology, which is coarser than the Fine Zeeman Topology $F$. The causal curves in a spacetime under $Z$ are piecewise null. $F$ is considered to be the most physical topology in a spacetime…

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…

The gravitational collapse of an infinite cylindrical thin shell of generic matter in an otherwise empty spacetime is considered. We show that geometries admitting two hypersurface orthogonal Killing vectors cannot contain trapped surfaces…

In this article we prove a global result in the spirit of Basener's theorem regarding the relation between q-pseudoconvexity and q-holomorphic convexity: we prove that any smoothly bounded strictly q-pseudoconvex open subset of the complex…

We analyze the causal structure of horizonless compact objects via the light-cone geometry and conformal compactification of the Joshi-Malafarina-Narayan (JMN-1) and Janis-Newman-Winicour (JNW) spacetimes. Penrose diagrams reveal that JMN-1…

It is still uncertain whether the cosmic censorship conjecture is true or not. To get a new insight into this issue, we propose the concept of the border of spacetime as a generalization of the spacetime singularity and discuss its…

This paper continues the investigations of noncommutative ordered spaces put forward by one of the authors. These metaphoric spaces are defined dually by so-called \emph{isocones} which generalize to the noncommutative setting the convex…