Related papers: Semi-analytical approach for the Vaidya metric in …
The general analytical solution for the static spherically symmetric metric supported by a perfect fluid with proportional-equation-of-state $p = w \rho$ is not known at the time of this writing, except for the trivial cases $w=0$ and…
We prove the persistence of analyticity for classical solution of the Cauchy problem for quasilinear wave equations with analytic data. Our results show that the analyticity of solutions, stated by the Cauchy-Kowalewski and…
This article investigates on the radial and non-radial geodesic structures of the generalized K-essence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal…
We revisit the method of kinematical endpoints for particle mass determination, applied to the popular SUSY decay chain squark -> neutralino -> slepton -> LSP. We analyze the uniqueness of the solutions for the mass spectrum in terms of the…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
The set of all possible spherically symmetric magnetic static Einstein-Yang-Mills field equations for an arbitrary compact semi-simple gauge group $G$ was classified in two previous papers. Local analytic solutions near the center and a…
The complete solution of Einstein's gravitational equations with a vacuum-vacuum Kerr-Schild pencil of metrics $g_{ab}+V l_al_b$ is obtained. Our result generalizes the solution of the Kerr-Schild problem with a flat metric $g_{ab}$…
We construct all axi-symmetric non-gradient $m$-quasi-Einstein structures on a two-sphere. This includes the spatial cross-section of the extreme Kerr black hole horizon corresponding to $m=2$, as well as a family of new regular metrics…
The asymptotic properties of conformally static metrics in Einstein-aether theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime,…
Using both numerical and analytical tools we study various features of static, spherically symmetric solutions of the Einstein-Vlasov system. In particular, we investigate the possible shapes of their mass-energy density and find that they…
We investigate in the present paper the Navier-Stokes equations on quantum Euclidean spaces $\mathbb{R}^d_{\theta}$ with $\theta$ being a $d\times d$ antisymmetric matrix, which is a standard example of non-compact noncommutative manifolds.…
Complete sequences of new analytic solutions of Einstein's equations which describe thin super massive disks are constructed. These solutions are derived geometrically. The identification of points across two symmetrical cuts through a…
We study static quantum corrections of the Schwarzschild metric in the Boulware vacuum state. Due to the absence of a complete analytic expression for the full semiclassical Einstein equations we approach the problem by considering the…
We present a method for generating exact interior solutions of Einstein's equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well…
The use of the sine-Gordon equation as a model of magnetic flux propagation in Josephson junctions motivates studying the initial-value problem for this equation in the semiclassical limit in which the dispersion parameter $\e$ tends to…
We define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance…
We present a stationary axially symmetric two parameter vacuum solution which could be considered as ``dual'' to the Kerr solution. It is obtained by removing the mass parameter from the function of the radial coordinate and introducing a…
We consider solutions of the semi-classical Einstein-Klein-Gordon system with a cosmological constant $\Lambda\in\mathbb{R}$, where the spacetime is given by Einstein's static metric on $\mathbb{R}\times\mathbb{S}^3$ with a round sphere of…
A solution for the Einstein gravity coupled with non linear electrodynamics is introduced in 2+1 dimensions. Especially, in the case with a non-vanishing cosmological constant, we obtain a novel black hole solution. To find fundamental…
Analytical solution of Weyl neutrino wave equation in Kerr geometry is presented by making use of the two-spinor component spin-coefficient Newman-Penrose (NP) calculus. So far only asymptotic or approximate solutions have been found for…