Related papers: Boundary contributions in the causal set action
The homogeneous causal action principle on a compact domain of momentum space is introduced. The connection to causal fermion systems is worked out. Existence and compactness results are reviewed. The Euler-Lagrange equations are derived…
We present two results which concern certain aspects of the question: when is a causal set well approximated by a Lorentzian manifold? The first result is a theorem which shows that the number-volume correspondence, if required to hold even…
The expression of causality depends on an underlying choice of chronology. Since a chronology is provided by any Lorentzian metric in relativistic theories, there are as many expressions of causality as there are non-conformally related…
We study branching Brownian motion in hyperbolic space. As hyperbolic Brownian motion is transient, the normalised empirical measure of branching Brownian motion converges to a random measure $\mu_\infty$ on the boundary. We show that the…
We prove that for any countable group acting virtually specially on a CAT(0) cube complex, the orbit equivalence relation induced by its action on the Roller boundary is hyperfinite. This can be considered as a generalization of…
A change of spatial topology in a causal, compact spacetime cannot occur when the metric is globally Lorentzian. One can however construct a causal metric from a Riemannian metric and a Morse function on the background cobordism manifold,…
We present two families of first-order in time and second-order in space formulations of the Einstein equations (variants of the Arnowitt-Deser-Misner formulation) that admit a complete set of characteristic variables and a conserved energy…
We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic…
The study of low regularity (in-)extendibility of Lorentzian manifolds is motivated by the question whether a given solution to the Einstein equations can be extended (or is maximal) as a weak solution. In this paper we show that a timelike…
Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
Using the method of images we derive the boundary term of the Einstein-$\Gamma^2$ action in half-space from the spherical worldsheet to first order in $\alpha'$ and to linear order in the metric perturbation around flat half-space. The…
We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on…
Holographic complexity, in the guise of the Complexity = Volume prescription, comes equipped with a natural correspondence between its rate of growth and the average infall momentum of matter in the bulk. This Momentum/Complexity…
We study some particular cases of Viterbo's conjecture relating volumes of convex bodies and actions of closed characteristics on their boundaries, focusing on the case of a Hamiltonian of classical mechanical type, splitting into summands…
This article investigates an extension of General Relativity based upon a class of lifted metrics on the cotangent bundle of space-time. The dynamics of the theory is determined by a fixed section of the cotangent bundle, representing the…
A consistent variational procedure applied to the gravitational action requires according to Gibbons and Hawking a certain balance between the volume and boundary parts of the action. We consider the problem of preserving this balance in…
For a certain class of genuinely nonlinear two-by-two planar hyperbolic systems we show that any classical solution on a smoothly bounded domain has nontangential boundary limits except on a set whose Hausdorff dimension is bounded by some…
This article gives a review of a recent construction, the ambient cosmological metric, and its implications for the global geometry of the universe. According to this proposal, the universe is a bounding hypersurface carrying a conformal…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…