Related papers: Interpolating the Schwarzschild and de-Sitter metr…
We establish a new uniqueness theorem for the three dimensional Schwarzschild-de Sitter metrics. For this some new or improved tools are developed. These include a reverse Lojasiewicz inequality, which holds in a neighborhood of the…
The purpose of this paper is threefold. First the natural extension of Riesz potentials to the context of quasi metric measure spaces for the class of upper doubling measures are studied on Lebesgue spaces, obtaining necessary and…
Under consideration of coordinate conditions, we get the Schwarzschild-Beltrami-de Sitter (S-BdS) metric solution of the Einstein field equations with a cosmological constant $\Lambda$. A brief review to the de Sitter invariant special…
Earlier constructed a simple nonlocal de Sitter gravity model has a cosmological solution in a very good agreement with astronomical observations. In this paper, we continue the investigation of the nonlocal de Sitter model of gravity,…
We show that mass parameter and radial coordinate values can be indirectly measured in thought experiments performed in Schwarzschild spacetime, without using the Newtonian limit of general relativity or approximations based on Euclidean…
Spacetime metrics describing `non-singular' black holes are commonly studied in the literature as effective modification to the Schwarzschild solution that mimic quantum gravity effects removing the central singularity. Here we point out…
We treat the general theory of nonlinear ideals and extend as many notions as possible from the linear theory to the nonlinear theory. We define nonlinear ideals with special properties which associate new non-linear ideals to given ones…
The Lenz-Sommerfeld argument allows an ingenious and simple derivation of the Schwarzschild solution of Einstein equations of general relativity. In this paper, we use the same reasoning to construct the de Sitter line element.
We propose a non-metastable de-Sitter infinitesimal patch as a replacement for the theoretical singularity that occurs during the description of maximally extended Schwarzschild Anti-de Sitter spacetimes. This corresponds to a highly…
We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized…
We revisit and improve the analytic study arXiv:1804.03462 of spherically symmetric but dynamical black holes in Einstein's gravity coupled to a real scalar field. We introduce a series expansion in a small parameter $\epsilon$ that…
In this paper we will analyse the inner product for gauge theories in de Sitter spacetime. This will be done by analysing an Euclidean version of the de Sitter metric. Thus, the de Sitter metric will be related to the metric on a…
We give the general Kerr-de Sitter metric in arbitrary spacetime dimension D\ge 4, with the maximal number [(D-1)/2] of independent rotation parameters. We obtain the metric in Kerr-Schild form, where it is written as the sum of a de Sitter…
We utilize the gravitational decoupling via the extended geometric deformation to extend the Schwarzschild vacuum solution to new black holes in Rastall theory. By employing linear transformations that deform both the temporal and radial…
The exterior and interior Schwarzschild solutions are rewritten replacing the usual radial variable with an angular one. This allows to obtain some results otherwise less apparent or even hidden in other coordinate systems.
The goal of this work is to introduce a local and a global interpolator in Jacobi-weighted spaces, with optimal order of approximation in the context of the $p$-version of finite element methods. Then, an a posteriori error indicator of the…
The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…
We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized…
Based on some important properties of $dS$ space, we present a Beltrami model ${\cal B}_\Lambda$ that may shed light on the observable puzzle of $dS$ space and the paradox between the special relativity principle and cosmological principle.…
The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject…