Related papers: $\gamma$-Metrics in Higher Dimensions
In a recent work [arXiv:2307.13489 [gr-qc]], we have described spherically symmetric and static quantum black holes as deformations of the classical Schwarzschild metric that depend on the physical distance to the horizon. We have developed…
We obtain a new, exact, solution of the Einstein's equation in higher dimensions. The source is given by a static spherically symmetric, Gaussian distribution of mass and charge. De-localization of mass and charge is due to the presence of…
The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy. We develop…
Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a…
: In studies of discrete structures, functions are frequently used that express proximity, but are not metrics. We consider a class of such functions that is characterized by a normalization condition and an inequality that plays the same…
This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
In this paper a new small parameter associated with the density matrix deformation (density pro-matrix)studied in previous works of the author is introduced into the Generalized Quantum Mechanics (GQM), i.e. quantum mechanics involving…
In this manuscript, we provide a concise review of the concept of metric dimension for both deterministic as well as random graphs. Algorithms to approximate this quantity, as well as potential applications, are also reviewed. This work has…
A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are…
We present a new model of dark energy which could explain the observed accelerated expansion of our Universe. We show that a five-dimensional Einstein-Yang-Mills theory defined in a flat Friedmann-Robertson-Walker universe compactified on a…
Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well-known to also be solutions in all spacetimes with conformally-related metrics. This provides a sense in which electromagnetism alone cannot be used to…
Einstein-Gauss-Bonnet gravity in five-dimensional spacetime provides an excellent example of a theory that, while including higher-order curvature corrections to General Relativity, still shares many of its features, such as second-order…
The key probes of the growth of large-scale structure are its rate $f$ and amplitude $\sigma_8$. Redshift space distortions in the galaxy power spectrum allow us to measure only the combination $f\sigma_8$, which can be used to constrain…
The {\em metric dimension} of a graph $\Gamma$ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph…
Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the metric. Then we construct a doubling metric for which the measure of a dillated ball is closely related to these dimensions.
An exact class of solutions of the 5D vacuum Einstein field equations (EFEs) is obtained. The metric coefficients are found to be non-separable functions of time and the extra coordinate $l$ and the induced metric on $l$ = constant…
The set of badly approximable $m \times n $ matrices is known to have Hausdorff dimension $mn $. Each such matrix comes with its own approximation constant $c$, and one can ask for the dimension of the set of badly approximable matrices…
We present a bi-metric theory of gravity containing a length scale of galactic size. For distances less than this scale the theory satisfies the standard tests of General Relativity. For distances greater than this scale the theory yields…
The standard theory of General Relativity (GR) currently provides the most reliable description of all gravitational events in Astrophysics and Cosmology. However, current Astronomy allows measurements that contradict the predictions of GR…