相关论文: Causally simple inextendible spacetimes are hole-f…
It is shown that if $M$ is a strongly causal free of naked singularities space-time, then its causal structure is completely characterized by a partial order in the space of skies defined by means of a class non-negative Legendrian…
We derive a formula for the spacetime volume of a small causal cone. We use this formula within the context of causal set theory to construct causal set expressions for certain geometric quantities relating to a spacetime with a spacelike…
All physical process are subject to some laws which determine with math accurately its time-space evolution. These laws are described, in the last analysis for the principle of causality. The physical space can be homogeneous or…
We consider a class of black holes for which the area of the two-dimensional spatial cross-section has a minimum on the horizon with respect to a quasiglobal (Krusckal-like) coordinate. If the horizon is regular, one can generate a tubelike…
Charged and/or rotating black holes in General Relativity feature Cauchy horizons, which indicate a breakdown of predictability in the theory. Focusing on spherically symmetric charged black holes, we remark that the inevitability of…
It is shown that if the timelike eigenvector of the Ricci tensor be hypersurface orthogonal so that the space time allows a foliation into space sections then the space average of each of the scalar that appear in the Raychaudhuri equation…
A hairy extension of the Bertotti-Robinson regular spacetime has been recently introduced in the context of the Einstein-Maxwell-Scaler theory that surprisingly is a singular black hole formed in the $S_{3}$ background spatial topology…
We give an example of a spacetime with a continuous metric which is globally hyperbolic and exhibits causal bubbling. The metric moreover splits orthogonally into a timelike and a spacelike part. We discuss our example in the context of…
We study numerically the evolution of spactime, and in particular of a spacetime singularity, inside a black hole under a class of perturbations of non-compact support. We use a very simplified toy model of a spherical charged black hole…
It is shown that if an asymptotically flat spacetime is asymptotically stationary, in the sense that $\Lie_{\xi} g_{ab}$ vanishes at the rate $\sim t^{-3}$ for asymptotically timelike vector field $\xi^a$, and the energy-momentum tensor…
In a causal world the direction of the time arrow dictates how past causal events in a variable $X$ produce future effects in $Y$. $X$ is said to cause an effect in $Y$, if the predictability (uncertainty) about the future states of $Y$…
The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime $(M,g)$ admits a smooth time…
In this contribution, we study spacetimes of cosmological interest, without making any symmetry assumptions. We prove a rigid Hawking singularity theorem for positive cosmological constant, which sharpens known results. In particular, it…
The extendibility of spacetime and the existence of weak solutions to the Einstein field equations beyond Cauchy horizons, is a crucial ingredient to examine the limits of General Relativity. Strong Cosmic Censorship serves as a firewall…
It is shown that the space of null geodesics of a star-shaped causally simple subset of Minkowski space is contactomorphic to the canonical contact structure in the spherical cotangent bundle of $\mathbb{R}^n$. In the $3$-dimensional case…
We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature $K$ are…
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating everywhere expanding universes with non-vanishing spatial average of the matter variables…
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…
A Theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say vacuum, space--times to some properties of the orbits near the Cauchy surface. In particular it is shown…
The conditions are clarified under which regular (i.e., singularity-free) black holes can exist. It is shown that in a large class of spacetimes that satisfy the weak energy condition the existence of a regular black hole requires topology…