Related papers: Volume comparison by timelike Lipschitz maps
If textbook Lorentz invariance is actually a property of the equations describing a sector of matter above some critical distance scale, several sectors of matter with different critical speeds in vacuum can coexist and an absolute rest…
Trans-Planckian redshifts in cosmology and outside black holes may provide windows on a hypothetical short distance cutoff on the fundamental degrees of freedom. In cosmology, such a cutoff seems to require a growing Hilbert space, but for…
Using the result of Petersen & Wink '21, we find obstructions to the curvature and topology of compact Lorentzian manifolds admitting a unit-length timelike Killing vector field.
In this work we revisit the notion of the (future) causal completion of a globally hyperbolic spacetime and endow it with the structure of a Lorentzian pre-length space. We further carry out this construction for a certain class of…
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…
The concept of a hyperuniformity disorder length $h$ was recently introduced for analyzing volume fraction fluctuations for a set of measuring windows. This length permits a direct connection to the nature of disorder in the spatial…
We begin with a basic exploration of the (point-set topological) notion of Hausdorff closed limits in the spacetime setting. Specifically, we show that this notion of limit is well suited to sequences of achronal sets, and use this to…
The support measures of a convex body are a common generalization of the curvature measures and the area measures. With respect to the Hausdorff metric on the space of convex bodies, they are weakly continuous. We provide a quantitative…
This paper carries out a renormalization of the volume of the Loewner-Nirenberg singular Yamabe metric in a given conformal class on a compact manifold-with-boundary. This generalizes the usual volume renormalization for Poincare-Einstein…
In this note we continue the analysis of metric measure space with variable ricci curvature bounds. First, we study $(\kappa,N)$-convex functions on metric spaces where $\kappa$ is a lower semi-continuous function, and gradient flow curves…
We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…
In this paper we scrutinize the concept of locally inertial reference frames (LIRF) in Lorentzian and Riemann-Cartan spacetime structures. We present rigorous mathematical definitions for those objects, something that needs preliminary a…
Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connection, which is locally but not globally Levi-Civita. The…
Uniqueness (up to isometries) and existence of limits are studied in the context of Cheeger-Gromov convergence of spacetimes. To address the non-compactness of the vector isometry group in the semi-Riemannian setting, standard pointed…
Let N be a (n+1)-dimensional globally hyperbolic Lorentzian manifold with a compact Cauchy hypersurface. We consider curvature flows in N with different curvature functions F (including the mean curvature, the gauss curvature and the second…
A clock synchronization thought experiment is modeled by a diffeomorphism invariant "time delay" observable. In a sense, this observable probes the causal structure of the ambient Lorentzian spacetime. Thus, upon quantization, it is…
Recently, a link between Lorentzian and Finslerian Geometries has been carried out, leading to the notion of wind Riemannian structure (WRS), a generalization of Finslerian Randers metrics. Here, we further develop this notion and its…
A structured collection of thought provoking conclusions about space and time is given. Using only the Compton wavelength lambda = hbar / m c and the Schwarzschild radius r_s = 2 G m / c^2, it is argued that neither the continuity of…
Gravitational wave astronomy relies on the use of multiple detectors, so that coincident detections may distinguish real signals from instrumental artifacts, and also so that relative timing of signals can provide the sky position of…
We provide new similarities between regular continued fractions and L\"uroth series in terms of topological dynamics and Hausdorff dimension. In particular, we establish a complete analogue for the L\"uroth transformation of results by W.…