Related papers: Brill-Lindquist-Riemann sums and their limits
This analysis considers our universe as a closed Friedmann universe, dominated by vacuum energy in the form of a cosmological constant, with cosmological parameters obtained from full mission Planck satellite observations. A few simple…
We revise general relativity (GR) from the perspective of calculus for moving surfaces (CMS). While GR is intrinsically constructed in pseudo-Riemannian geometry, a complete understanding of moving manifolds requires embedding in a higher…
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…
By using simplified 2D gravitational, non-local Lorentz invariant actions constructed upon the torsion tensor, we discuss the physical meaning of the remnant symmetries associated with the near-horizon (Milne) geometry experienced by a…
We consider light propagation in an inhomogeneous irrotational dust universe with vanishing cosmological constant, with initial conditions as in standard linear perturbation theory. A non-perturbative approach to the dynamics of such a…
The generic properties of compact objects made of two different fluids of dark matter are studied in a scale invariant approach. We investigate compact objects with a core-shell structure, where the two fluids are separated, and with mixed…
We study a particular exact solution to the Born-Infeld determinantal gravity consisting of a cosmological model which undergoes a brusque bounce. The latter consists of an event characterized by a non-null (but finite) value of the squared…
On small scales the observable Universe is highly inhomogeneous, with galaxies and clusters forming a complex web of voids and filaments. The optical properties of such configurations can be quite different from the perfectly smooth…
In this paper, we identify two fractals if and only if they are biLipschitz equivalent. Fix ratio $r,$ for dust-like graph-directed sets with ratio $r$ and integer characteristics, we show that they are rigid in the sense that they are…
This thesis discusses exotic 7-spheres, i.e. manifolds that are homeomorphic but not diffeomorphic to the ordinary 7-sphere, using a set of analytical and computational tools from theoretical physics. The theory of fibre bundles and…
A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this…
In this paper, we investigate the caustic point developed by outgoing null hypersurfaces and the behavior of null curves. We analyze three cases: Future, past, and zero caustic point terminology for outgoing null hypersurfaces in the…
In this paper geometry of Gromov-Hausdorff distance on the class of all metric spaces considered up to an isometry is investigated. For this class continuous curves and their lengths are defined, and it is shown that the Gromov-Hausdorff…
Hilbert spaces in theories of gravity are notoriously subtle due to the Hamiltonian constraints, particularly regarding the inner product. To demystify this subject, we review and extend a collection of ideas in canonical gravity, and…
In a recent article PRD 111, 064001 (2025) a new geometric a approach for studying massive particle surfaces was proposed. Using the Gaussian and geodesic curvatures of a two dimensional Riemannian metric a criteria for the existence of…
Ricci-Curbastro established necessary and sufficient conditions for a Riemannian metric on a surface to be the first fundamental form of a minimal immersion of that surface into the Euclidean space. We revisit certain developments arising…
We start from a static, spherically symmetric space-time in the presence of an electrostatic field and construct the mini-superspace Lagrangian that reproduces the well known Reissner - Nordstr\"om solution. We identify the classical…
We introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum compact metric spaces, which extends the Gromov-Hausdorff distance to noncommutative geometry and strengthens Rieffel's quantum Gromov-Hausdorff distance…
The aim of this paper to introduce the reader to a recent point of view on the Lipschitz classifications of complex singularities. It presents the complete classification of Lipschitz geometry of complex plane curves singularities and in…
In this article we prove that the set of flat singular points of locally highest density of area-minimizing integral currents of dimension $m$ and general codimension in a smooth Riemannian manifold $\Sigma$ has locally finite…