Analytically Periodic Solutions to the 3-dimensional Euler-Poisson Equations of Gaseous Stars with Negative Cosmological Constant

TL;DR

This paper constructs novel time-periodic solutions to the 3D Euler-Poisson equations with a negative cosmological constant, extending classical models of stellar collapse to include periodic re-collapsing behavior.

Contribution

It introduces the first known self-similar, time-periodic solutions with negative cosmological constant for the Euler-Poisson equations, extending classical solutions to new dynamic regimes.

Findings

Existence of time-periodic, almost re-collapsing solutions

Extension of classical solutions to include negative cosmological constant

Conjecture of a new re-collapsing stellar model

Abstract

By the extension of the 3-dimensional analytical solutions of Goldreich and Weber "P. Goldreich and S. Weber, Homologously Collapsing Stellar Cores, Astrophys, J. 238, 991 (1980)" with adiabatic exponent gamma=4/3, to the (classical) Euler-Poisson equations without cosmological constant, the self-similar (almost re-collapsing) time-periodic solutions with negative cosmological constant (lambda<0) are constructed. The solutions with time-periodicity are novel. On basing these solutions, the time-periodic and almost re-collapsing model is conjectured, for some gaseous stars. Key Words: Analytically Periodic Solutions, Re-collapsing, Cosmological Constant, Euler-Poisson Equations, Collapsing