Solitons in the Einstein universe

TL;DR

This paper demonstrates the existence of gravitostatic wave solutions, including solitons and lattice structures, in the Einstein universe within Newtonian hydrodynamics incorporating Einstein's cosmological constant.

Contribution

It introduces new gravitostatic wave solutions, including solitons and Zeldovich pancake lattices, in the context of Einstein's static universe with Newtonian hydrodynamics.

Findings

Existence of steady-state density singularities as wave solutions.

Identification of solitons at the Einstein universe density.

Lattice of Zeldovich pancakes as nonlinear gravitational structures.

Abstract

We show that equations of Newtonian hydrodynamics and gravity with Einstein's cosmological constant included admit gravitostatic wave solutions propagating in the background of Einstein's static Universe. In the zero pressure limit these waves exist at an average matter density exceeding that of Einstein's Universe. They have the form of a lattice of integrable density singularities localized at the maxima of the gravitational potential. These singularities are steady-state counterparts of the so-called Zeldovich pancakes (ZP), interim wall-like structures appearing at nonlinear stages of development of gravitational instability. As the average matter density decreases, the period of the ZP lattice increases diverging at the density of Einstein's Universe. Solitary wave solutions are found at exactly the density of Einstein's Universe, and at a slightly larger density the wave may be viewed as a lattice of well-separated ZP solitons.