An exact self-similar solution for an expanding ball of radiation
نویسنده
چکیده
We give an exact solution of the 5D Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation of state of radiation. The matter satisfies the usual energy and thermodynamic conditions. The energy density and temperature are related by the Stefan-Boltzmann law. The solution admits a homothetic Killing vector in 5D, which induces the existence of self-similar symmetry in 4D, where the line element as well as the dimensionless matter quantities are invariant under a simple “scaling” group. PACS: 04.50.+h; 04.20.Cv
منابع مشابه
ar X iv : g r - qc / 0 40 20 46 v 1 1 0 Fe b 20 04 An exact self - similar solution for an expanding ball of radiation
We give an exact solution of the 5D Einstein equations which in 4D can be interpreted as a spherically symmetric distribution of matter, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation of state of radiation. The solution admits a homothetic Killing vector in 5D, which induces the existence of self-similar symmetry in 4D, where the line element as well as...
متن کاملAixsymmetric Stagnation Point Flow of a Viscous Fluid on a Moving Cylinder with Time Dependent Axial Velocity
The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite moving cylinder with time-dependent axial velocity is investigated. The impinging free stream is steady with a strain rate k. An exact solution of the Navier-Stokes equations is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations. The general self-si...
متن کاملExact Analytical Solution for Bending Analysis of Functionally Graded Annular Sector Plates
In this article, an exact levy solution is presented for bending analysis of a functionally graded (FG) annular sector plate. The governing equilibrium equations are obtained based on the classical plate theory. Introducing an analytical method for the first time, the three coupled governing equilibrium equations are replaced by an independent equation in term of transverse deflection. This equ...
متن کاملAn Exact Solution for Vibration Analysis of Soft Ferromagnetic Rectangular Plates Under the Influence of Magnetic Field with Levy Type Boundary Conditions
In this paper vibration of ferromagnetic rectangular plates which are subjected to an inclined magnetic field is investigated based on classical plate theory and Maxwell equations. Levy type solution and Finite element method using Comsol software are used to obtain the frequency of the plate subjected to different boundary conditions, good agreements is obtained when computed results are compa...
متن کاملA point explosion in a freely expanding medium
We present an exact invariant solution for a point explosion in an inertially expanding medium. The blast wave dynamics continuously joins the self-similar Sedov asymptotics at early times and asymptotical comoving with the ambient medium at late times. The applications to galactic supershell blowout dynamics and cosmological explosions are discussed.
متن کامل