Gravitational evolution of a perturbed lattice and its fluid limit
Abstract
We apply a simple linearisation, used standardly in solid state physics, to give an approximation describing the evolution under its self-gravity of an infinite perfect lattice perturbed from its equilibrium. In the limit that the initial perturbations are restricted to wavelengths much larger than the lattice spacing, the evolution corresponds exactly to that derived from an analagous linearisation of the Lagrangian formulation of the dynamics of a pressureless self-gravitating fluid, with the Zeldovich approximation as a sub-class of asymptotic solutions. Our less restricted approximation allows one to trace the evolution of the fully discrete distribution until the time when particles approach one another (i.e. ``shell crossing''), with modifications of the fluid limit explicitly depending on the lattice spacing. We note that the simple cubic lattice presents both oscillating modes and modes which grow faster than in the fluid limit.Keywords
All Related Versions
This publication has 0 references indexed in Scilit: