Related papers: The Szekeres metrics with $M < 0$
This manuscript deals with a model of the evolution of an event space represented by the fundamental solution of a N-dimensional generalized Schrodinger equation for free matter. Specifically this solution can be applied to describe the 3D…
An improved upper bound is obtained for the density of sequences of positive integers that contain no k-term geometric progression.
We consider a quantum mechanical black hole model introduced in {\it Phys.Rev.}, {\bf D57}, 1118 (1998) that consists of the selfgravitating dust shell. The Schroedinger equation for this model is a finite difference equation with the shift…
Numerous confirmations may indicate that, besides the problem of Higgs sector many external parameters, the Standard Model is a complete low energy particle interaction theory not crying for new physics. But there are serious problems with…
Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition collapses to the extent a closed trapped surface is formed, a singularity is…
Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly…
The full metric describing a stationary axisymmetric system of two arbitrary Kerr sources, black holes or hyperextreme objects, located on the symmetry axis and kept apart in equilibrium by a massless strut is presented in a concise…
We consider solutions of the Einstein equations with cosmological constant $\Lambda\neq 0$ admitting conformal compactification with smooth scri $\mathscr{I^+}$. Metrics are written in the Bondi-Sachs coordinates and expanded into inverse…
We show that requiring unbroken supersymmetry everywhere in black-hole-type solutions of N=2,d=4 supergravity coupled to vector supermultiplets ensures in most cases absence of naked singularities. We show that the requirement of global…
The equations of the 1+3 orthonormal frame approach are explicitly presented and discussed. Natural choices of local coordinates are mentioned. A dimensionless formulation is subsequently given. It is demonstrated how one can obtain a…
The spectral energy distribution (SED) of galaxies provides fundamental information on the related physical processes. However, the SED is significantly affected by dust in its interstellar medium. Dust is mainly produced by asymptotic…
The necessary and sufficient condition for the absence of particle horizons in a big bang Friedmann-Robertson-Walker universe is provided. It happens to be a "smooth big bang" initial condition: the proper time derivative of the expansion…
Global properties of static, spherically symmetric configurations of scalar fields of sigma-model type with arbitrary potentials are studied in $D$ dimensions, including space-times containing multiple internal factor spaces. The latter are…
The question of whether the zero viscosity limit $\nu\to 0$ is identical to the no viscosity $\nu\equiv 0$ case is investigated in a simple shell (GOY) model with only three shells. We find that it is possible to express two velocities in…
This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have…
This paper is concerned with the global boundedness and blowup of solutions to the Keller-Segel system with density-dependent motility in a two-dimensional bounded smooth domain with Neumman boundary conditions. We show that if the motility…
We define a continuum percolation model that provides a collection of random ellipses on the plane and study the behavior of the covered set and the vacant set, the one obtained by removing all ellipses. Our model generalizes a construction…
In this paper we try to clarify that a regular metric can generate a singular spacetime. Our work focuses on a static and spherically symmetric spacetime in which regularity exists when all components of the Riemann tensor are finite. There…
We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a…
The full metric describing two counter-rotating identical Kerr black holes separated by a massless strut is derived in the explicit analytical form. It contains three arbitrary parameters which are the Komar mass M, Komar angular momentum…