Related papers: Remarks on the distributional Schwarzschild geomet…
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…
In this paper we analyze the spacetime geometry due to a Schwarzschild object having uniform accelerated motion. In the beginning, we investigate the gravitational field due to a uniformly moving Schwarzschild object and obtain the…
We consider the revised Deser-Woodard model of nonlocal gravity by reformulating the related field equations within a suitable tetrad frame. This transformation significantly simplifies the treatment of the ensuing differential problem…
The behavior of isothermal plasma waves has been analyzed near the Schwarzschild horizon. We consider a non-rotating background with non-magnetized and magnetized plasmas. The general relativistic magnetohydrodynamical equations for the…
A new spherically-symmetric solution is determined in a noncompactified Kaluza-Klein theory in which a time character is ascribed to the fifth coordinate. This solution contains two independent parameters which are related with mass and…
Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…
This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…
The Tolman~VII solution, an exact analytic solution to the spherically symmetric, static Einstein equations with a perfect fluid source, has many characteristics that make it interesting for modelling high density physical astronomical…
Following Geroch, Traschen, Mars and Senovilla, we consider Lorentzian manifolds with distributional curvature tensor. Such manifolds represent spacetimes of general relativity that possibly contain gravitational waves, shock waves, and…
The electric and magnetic fields of a pole-dipole singularity attributed to a point-electron-singularity in the Maxwell field are expressed in a Colombeau algebra of generalized functions. This enables one to calculate dynamical quantities…
It is shown how the use of the Kerr-Schild coordinate system can greatly simplify the formulation of the geodesic equation of the Schwarzschild solution. An application of this formulation to the numerical computation of the aspect of a…
GR and other metric theories of gravity are formulated with an arbitrary auxiliary curved background in a Lagrangian formalism. A new sketch of how to include spinor fields is included. Conserved quantities are obtained using Noether's…
We study the particular case in which Extended Geometric Deformation does consists of consecutive deformations of temporal and spatial components of the metric, in Schwarzschild-like and isotropic coordinates. In the latter, we present two…
We show that the dynamics of Schwarzschild-(A)dS black holes admits a symmetry under the 2d Schr\"odinger group, whatever the sign or value of the cosmological constant. This is achieved by reformulating the spherically-symmetric reduction…
In this work we have obtained the set of new exact solutions of the Einstein equations that generalize the known Lemaitre-Tolman-Bondi solution for the certain case of nonzero pressure under zero spatial curvature. These solutions are…
We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…
We give the regularization for fractional integral by delta sequence and apply it to obtain existence-uniqueness theorems in Colombeau algebras for nonlinear equations with singularities: nonlinear system of integral equations with polar…
We describe a non-minimal higher-derivative extension of Einstein-Maxwell theory in which electrically-charged black holes and point charges have globally regular gravitational and electromagnetic fields. We provide an exact static…
The electrostatic potential of any test charge distribution in Schwarzschild space with boundary values is derived. We calculate the Green's function, generalize the second Green's identity for p-forms and find the general solution.…
Static spherically symmetric distributions of electrically counterpoised dust (ECD) are used to construct solutions to Einstein-Maxwell equations in Majumdar--Papapetrou formalism. Unexpected bifurcating behaviour of solutions with regard…