Related papers: Causal structure and topology change in (2+1)-dime…
The event horizon of a black hole is arguably the most dramatic manifestation of the fact that in General Relativity, causal structure is dynamical and spacetimes can be separated into distinct regions by causal boundaries. Causal set…
We study the constraints coming from local causality requirement in various $2+1$ dimensional dynamical theories of gravity. In topologically massive gravity, with a single parity non-invariant massive degree of freedom, and in new massive…
We study the charged black hole solutions of a 2+1 nonlinear electrodynamical theory with cosmological constant. Considered as a one-parameter group of theories (the exponent of the squared Maxwell tensor) the causal structure of all…
Recent results on causality in noncommutative space-time are reviewed. We study, in particular, quantum causal structures in 1+1 dimensional kappa Minkowski space-time. This later is described by a twisted Lorentzian Spectral Triple build…
The recent progress in the Causal Dynamical Triangulations (CDT) approach to quantum gravity indicates that gravitation is nonperturbatively renormalizable. We review some of the latest results in 1+1 and 3+1 dimensions with special…
Lorentzian topology change may be resolved into an ordered sequence of localized, orientation-sensitive operations rather than treated solely as a global transition between spatial manifolds. We develop a generator-history framework in…
A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal…
Three-dimensional Lorentzian quantum gravity, expressed as the continuum limit of a nonperturbative sum over spacetimes, is tantalizingly close to being amenable to analytical methods, and some of its properties have been described in terms…
2+1 gravity for spacetimes with topology RxT^2 has been much studied. We add a description of how to extend these spacetimes across a Cauchy horizon into a region where the torus becomes Lorentzian. The result is a one parameter family of…
We propose a new method of discovering causal structures, based on the detection of local, spontaneous changes in the underlying data-generating model. We analyze the classes of structures that are equivalent relative to a stream of…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
Recently, there have been several applications of differential and algebraic topology to problems concerned with the global structure of spacetimes. In this paper, we derive obstructions to the existence of spin-Lorentz and pin-Lorentz…
Motivated by the search for new observables in nonperturbative quantum gravity, we consider Causal Dynamical Triangulations (CDT) in 2+1 dimensions with the spatial topology of a torus. This system is of particular interest, because one can…
In these two lectures I describe the difficulties one encounters when trying to construct a framework in which to describe topology change in classical general relativity where one sticks to the assumption of an everywhere non-singular…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
We explicitly compute the causal structure of the Schwarzschild black hole spacetime, by providing an algorithm to decide if any pair of events is causally related. The primary motivation for this study comes from discrete quantum gravity,…
We investigate the impact of spatial topology in 3+1 dimensional causal dynamical triangulations (CDT) by performing numerical simulations with toroidal spatial topology instead of the previously used spherical topology. In the case of…
We present a short review of geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with causal structure related to special and general theory of relativity. We describe Lie…
Simplicial complexes are increasingly used to understand the topology of complex systems as different as brain networks and social interactions. It is therefore of special interest to extend the study of percolation to simplicial complexes.…
We present a concise new definition of Finsler spacetimes that generalize Lorentzian metric manifolds and provide consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces we show that…