Related papers: The Geometry of Small Causal Cones

We derive the gravitational Hamiltonian starting from the Gauss-Bonnet action, keeping track of all surface terms. This is done using the language of orthonormal frames and forms to keep things as tidy as possible. The surface terms in the…

The Gaussian surface area measures for $C$-pseudo-cones are studied in this paper. Using the variational arguments and the approximation methods of Schneider, we obtain the existence of solutions to the Gaussian-Minkowski problem for…

We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal…

The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional…

We consider the problem of determination of a volume of some bounded space-like hypersurfaces in the case of spherically symmetric spacetimes. In the case when the hypersurfaces is cut or bounded by a light-like hypersurface the problem may…

The causal set action of dimension $d$ is investigated for causal sets that are Poisson sprinklings into submanifolds of $d$-dimensional Minkowski space. Evidence, both analytic and numerical, is provided for the conjecture that the mean of…

We prove that `volume cone implies metric cone' in the setting of RCD spaces, thus generalising to this class of spaces a well known result of Cheeger-Colding valid in Ricci-limit spaces.

We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each…

Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…

Tube formulas (by which we mean an explicit formula for the volume of an $\epsilon$-neighbourhood of a subset of a suitable metric space) have been used in many situations to study properties of the subset. For smooth submanifolds of…

We perform numerical simulations of the approach to spacetime singularities. The simulations are done with sufficient resolution to resolve the small scale features (known as spikes) that form in this process. We find an analytical formula…

The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M,g) is a poset (M,<), with the order relation < corresponding to the spacetime causal relation. Spacetime…

We give a formula in terms of multidimensional resultants for an equation for the flex locus of a projective hypersurface, generalizing a classical result of Salmon for surfaces. Using this formula, we compute the dimension of this flex…

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,…

Let $V_{g,m,n}(\overrightarrow L,\overrightarrow \theta)$ be the Weil-Petersson volume of the moduli space of hyperbolic surfaces of genus g with m geodesic boundary components of length $\overrightarrow L=(\ell_1,...,\ell_m)$ and $n$ cone…

The goal of this work, motivated by the desire to understand causality in classical and quantum gravity, is an in depth investigation of causality in classical field theories with quasilinear equations of motion, of which General Relativity…

We study the relativistic quantum mechanical scattering of a bosonic particle by an infinite straight cosmic string, considering the non-minimal coupling between the bosonic field and the scalar curvature. In this case, an effective…

We examine general features of causal wedges in asymptotically AdS spacetimes and show that in a wide variety of cases they have non-trivial topology. We also prove some general results regarding minimal area surfaces on the causal wedge…

We give a short, case-free and combinatorial proof of de Concini and Procesi's formula for the volume of the simplicial cone spanned by the simple roots of any finite root system. The argument presented here also extends their formula to…

Causal set theory offers a simple and elegant picture of discrete physics. But the vast majority of causal sets look nothing at all like continuum spacetimes, and must be excluded in some way to obtain a realistic theory. I describe recent…