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The spacetime around astrophysical black holes is thought to be described by the Kerr solution. However, even within general relativity, there is not yet a proof that the final product of the complete collapse of an uncharged body can only…
We analyze the transformation of a very broad class of metrics that can be expressed in terms of static coordinates. Starting from a general ansatz, we obtain a relation for the parameters in which one can impose further symmetries or…
In this Letter, we have developed a numerically efficient framework for evaluating parameters in metric theories of gravity, and applied it to constrain the horizon-scale magnetic field in the Kerr-Bertotti-Robinson (Kerr-BR) spacetime…
I tell about different mathematical tool that is important in general relativity. The text of the book includes definition of geometrical object, concept of reference frame, geometry of metric-affinne manifold. Using this concept I learn…
We establish stability estimates for the $k$-plane transform on positive Radon measures, with particular emphasis on Fourier and Wasserstein metrics. We first introduce a metric on $k$-plane data and prove a bi-Lipschitz stability estimate…
So far the only seemingly significant indication of a cosmological variation exists for the proton-to-electron mass ratio as stated by Reinhold et al. (2006). The measured indication of variation is based on the combined analysis of H2…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…
There is an explicit resolution of the Poisson reduction of four planar point vortices, in the case that three of the vortex strengths are equal and the total vorticity is zero. The resolution, a Hamiltonian system on a unified symplectic…
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
Electric and magnetic Hertz potentials are a formalism for obtaining solutions of Maxwell's equations from solutions of the inhomogeneous wave equation, with polarisation and magnetisation as the sources. We provide an overview of their…
We formulate the nonminimal aether-modified gravity whose action represents itself as a sum of the usual Einstein-Hilbert action and the CPT-even Lorentz-breaking aether-like gravity term proposed by Carroll. For this theory, we show that…
We proceed to investigate the solutions of generalized supergravity equations (GSE) in three dimensions. Our candidate is the metric of BTZ black hole. It is shown that only the cases with $J=M=0$ and $J=0,~ M\neq 0$ of the BTZ metric…
We investigate two general relativistic effects - namely, the Shirokov and Shapiro effects - within the framework of the Zipoy-Voorhees spacetime ($q$-metric), which generalizes the Schwarzschild solution by incorporating a quadrupole…
The present paper establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of whether (quantitative) absolute continuity of the elliptic…
In a teleparallel theory of (2+1)-dimensional gravity developed in a previous paper, we examine generators of internal Lorentz transformations and of general affine coordinate transformations for static circularly symmetric exact solutions…
We study the integrability and equivalence of a generalized Heisenberg ferromagnet-type equation (GHFE). The different forms of this equation as well as its reduction are presented. The Lax representation (LR) of the equation is obtained.…
We present a systematic study of static solutions of the vacuum Einstein equations with negative cosmological constant which asymptotically approach the generalized Kottler (``Schwarzschild--anti-de Sitter'') solution, within (mainly) a…
The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its…
The light propagation in plasma medium around stationary gravitating objects is studied in the geometrical optics limit. Static metrics with quadrupole moments are considered, however, the main attention is paid to the stationary…