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We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex…
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques,…
Spacetimes with everywhere vanishing curvature tensor, but with torsion different from zero only on world sheets that represent closed loops in ordinary space are presented, also defects along open curves with end points at infinity are…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…
Black hole complementarity requires that the interior of a black hole be represented by the same degrees of freedom that describe its exterior. Entanglement plays a crucial role in the reconstruction of the interior degrees of freedom. This…
This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this…
We prove a large-data semi-global existence theorem and the dynamical formation of trapped surfaces for the Einstein-massless Vlasov system in 3+1 dimensions, without any symmetry assumptions. The analysis critically hinges on a finely…
One would expect spacetime to have a foam-like structure on the Planck scale with a very high topology. If spacetime is simply connected (which is assumed in this paper), the non-trivial homology occurs in dimension two, and spacetime can…
It is logically possible that regularly evaporating black holes exist in nature. In fact, the prevalent theoretical view is that these are indeed the real objects behind the curtain in astrophysical scenarios. There are several proposals…
We recast the system of Einstein field equations for Locally Rotationally Symmetric spacetimes into an autonomous system of covariantly defined geometrical variables. The analysis of this autonomous system gives all the important global…
We consider the causal structure of generalized uncharged McVittie spacetimes with increasing central mass $m (t)$ and positive Hubble factor $H (t)$. Under physically reasonable conditions, namely, a big bang singularity in the past, a…
In this paper a theorem is derived in order to provide a wide sufficient condition for an orthogonally transitive cylindrical spacetime to be singularity-free. The applicability of the theorem is tested on examples provided by the…
A model unifying general relativity with quantum mechanics is further developed. It is based on a noncommutative geometry which supposedly modelled the universe in its pre-Planckian epoch. The geometry is totally nonlocal with no time and…
We observed a phase transition-like behavior that is marked by the onset of the realization of the connectivity between two sites on a two-dimensional cross-section of a three-dimensional percolation cluster. This was found using…
Closed time-like curves naturally appear in a variety of chronology-violating space-times. In these space-times, the Principle of Self-Consistency demands an harmony between local and global affairs that excludes grandfather-like paradoxes.…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
The interaction of a cosmic string with a four-dimensional stationary black hole is considered. If a part of an infinitely long string passes close to a black hole it can be captured. The final stationary configurations of such captured…
The interaction of a cosmic string with a four-dimensional stationary black hole is considered. If a part of an infinitely long string passes close to a black hole it can be captured. The final stationary configurations of such captured…
We study higher dimensional gravitational collapse to topological black holes in two steps. Firstly, we construct some (n+2)-dimensional collapsing space-times, which include generalised Lemaitre-Tolman-Bondi-like solutions, and we prove…
Using a second law of complexity, we prove a black hole singularity theorem. By introducing the notion of trapped extremal surfaces, we show that their existence implies null geodesic incompleteness inside globally hyperbolic black holes.…