Related papers: Dynamical Spacetimes from Numerical Hydrodynamics
We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of…
We consider spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant in five dimensions and analyze evolution of small perturbations of anti-de Sitter spacetime using the recently proposed resonant…
We simulate the mesoscopic dynamics of droplets formed by phase separated fluids at nanometer scales where thermal fluctuations are significant. Both spherical droplets fully immersed in a second fluid and sessile droplets which are also in…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We consider Kasner space-time describing anisotropic three dimensional expansion of the fluid and obtain the dissipative evolution equations for shear stress tensor and energy density from kinetic theory. For this, we use the iterative…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
The special conformal transformation (composed by inversion - translation - inversion) is used to generate a time dependent conformally flat spacetime. In order to be an exact solution of Einstein's equations, we need as a source a stress…
We construct a discrete model of fluid particles according to the GENERIC formalism. The model has the form of Smoothed Particle Hydrodynamics including correct thermal fluctuations. A slight variation of the model reproduces the…
Characteristic methods show excellent promise in the evolution of single black hole spacetimes. The effective coupling with matter fields may help the numerical exploration of important astrophysical systems such as neutron star black hole…
Hydrodynamic self-similar solutions, as obtained by Chi [J. Math. Phys. 24, 2532 (1983)] have been generalized by introducing new variables in place of the old space and time variables. A systematic procedure of obtaining a complete set of…
We describe a method, using periodic points and determinants, for giving alternative expressions for dynamical quantities (including Lyapunov exponents and Hausdorff dimension of invariant sets) associated to analytic hyperbolic systems.…
The phenomenon of finite time blow-up in hydrodynamic partial differential equations is central in analysis and mathematical physics. While numerical studies have guided theoretical breakthroughs, it is challenging to determine if the…
Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this paper, we use asymmetric ideas and moving frames to solve the two-dimensional Boussinesq equations with partial…
Some of the most interesting scenarios that can be studied in astrophysics, contain fluids and plasma moving under the influence of strong gravitational fields. To study these problems it is required to implement numerical algorithms robust…
For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as…
We quantize the particle dynamics in AdS_{N+1} x S^M spacetime in static gauge, which leads to the coordinate representation with wave functions depending only on spatial coordinates. The energy square operator is quadratic in canonical…
We describe how analytic solutions for linear hydromagnetic waves can be used for testing cosmological magnetohydrodynamic (MHD) codes. We start from the comoving MHD equations and derive analytic solutions for the amplitude evolution of…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
We present a numerical study of the Einstein equations, according to the Arnowitt-Deser-Misner (ADM) formalism, in order to simulate the dynamics of gravitational fields. We took in consideration the original $3+1$ decomposition of the ADM…
A method of solving perfect fluid Einstein equations with two commuting spacelike Killing vectors is presented. Given a spacelike 2-dimensional surface in the 3-dimensional nonphysical Minkowski space the field equations reduce to a single…