Related papers: Horizons Inside Classical Lumps
Classical linear wave superposition produces the appearance of interference. This observation can be interpreted in two equivalent ways: one can assume that interference is an illusion because input components remain unperturbed, or that…
We present here a large collection of harmonic and quadratic harmonic sums, that can be useful in applied questions, e.g., probabilistic ones. We find closed-form formulae, that we were not able to locate in the literature.
Isolated horizons are a quasi-local framework, developed over the last 15 years by many authors, for modeling black holes `in equilibrium' that involves assumptions only about geometric structures intrinsic to the horizon. We review the…
Wormholes are hypothetical topologically-non-trivial structures of the spacetime. From the theoretical point of view, the possibility of their existence is challenging but cannot be ruled out. This article is a compact and non-exhaustive…
Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.
This contains a list of (mostly very minor) corrections to the book Introduction to Symplectic Topology, Clarendon Press, Oxford, (1995), together with rewritten versions of two lemmas and some additional comments.
Editorial of a special issue on dark matter & modified gravity, distributed across the journals Studies in History and Philosophy of Modern Physics and Studies in History and Philosophy of Science. Published version of the open access…
This paper deals with certain fundamental results about affine hulls and simplices in a real normed linear space. The framework of the paper is Bishop's constructive mathematics, which, with its characteristic interpretation of existence as…
Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in vision-language understanding tasks. While these models often produce linguistically coherent output, they often suffer from hallucinations, generating…
We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature…
Ellipsoids possess several beautiful properties associated with classical potential theory. Some of them are well known, and some have been forgotten. In this article we hope to bring a few of the "lost" pieces of classical mathematics back…
There is persistent and endemic confusion between the true (future) horizon and the illusory (past) horizon of a black hole. The illusory horizon is the redshifting surface of matter that fell into the black hole long ago. A person who…
We construct motivic versions of the classical tubular neighborhood and the punctured tubular neighborhood, and give applications to the construction of tangential base-points for mixed Tate motives, algebraic gluing of curves with boundary…
This is a preprint version of a chapter for Handbook of Algebra.
In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those…
An idealised experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…
We present libsharp, a code library for spherical harmonic transforms (SHTs), which evolved from the libpsht library, addressing several of its shortcomings, such as adding MPI support for distributed memory systems and SHTs of fields with…
We examine the possible trajectories of a classical particle, trapped in a two-dimensional infinite rectangular well, using the Hamilton-Jacobi equation. We observe that three types of trajectories are possible: periodic orbits, open orbits…
Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…
We propose a generalization of the classical point-line Cremona-Richmond configuration to a configuration of points and more dimensional subspaces of a projective space, and present them as geometric realizations of some interesting…