Related papers: Shock Waves in Plane Symmetric Spacetimes
In this paper we shall discuss the backreaction of a massive quantum scalar field on the curvature, the latter treated as a classical field. Furthermore, we shall deal with this problem in the realm of cosmological spacetimes by analyzing…
We consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows…
In this paper we prove that for a certain class of initial data, smooth solutions of the hydrostatic Euler equations blow up in finite time.
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.…
A second-order PDE is derived from Euler's equaitons under certain assumptions. It is shown that this PDE admits shock and rarefaction waves, and that a single point gradient blow-up admits a unique similarity extension after blow-up that…
As it is well known, the global structure of the Einstein equations for general relativity in the context of the initial value problem, is a difficult and intricate mathematical problem. Therefore, any additional structure in their…
In this paper, we study the solitary wave and the Cauchy problem for Half-wave-Schr\"{o}dinger equations in the plane. First, we show the existence and orbital stability of the ground states. Secondly, we prove that traveling waves exist…
We solve a $1+5$-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the…
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of…
The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a…
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure, the spatial part of the dimensionless four-velocity and the particle density. Radially symmetric solutions of these equations are studied in two…
We obtain a system for the spatial metric and extrinsic curvature of a spacelike slice that is hyperbolic non-strict in the sense of Leray and Ohya and is equivalent to the Einstein equations. Its characteristics are the light cone and the…
Gravitational waves in cylindrically symmetric Einstein gravity are described by an effective energy tensor with the same form as that of a massless Klein- Gordon field, in terms of a gravitational potential generalizing the Newtonian…
We examine the dynamics of accelerating normal shocks in stratified planar atmospheres, providing accurate fitting formulae for the scaling index relating shock velocity to the initial density and for the post-shock acceleration factor as…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
We construct gravitating superconducting string solutions of the U(1)_{local} x U(1)_{global} model solving the coupled system of Einstein and matter field equations numerically. We study the properties of these solutions in dependence on…
In the special case of a spherically symmetric solution of Einstein equations coupled to a scalar massless field, we examine the consequences on the exact solution imposed by a semiclassical treatment of gravitational interaction when the…
It has been shown that if one solves self-consistently the semiclassical Einstein equations in the presence of a quantum scalar field, with a cutoff on the number of modes, spacetime become flatter when the cutoff increases. Here we extend…
The stability features of steady states of the spherically symmetric Einstein-Vlasov system are investigated numerically. We find support for the conjecture by Zeldovich and Novikov that the binding energy maximum along a steady state…