Analytically periodic solutions to the three-dimensional Euler–Poisson equations of gaseous stars with a negative cosmological constant

By extension of the three-dimensional analytical solutions of Goldreich and Weber (1980 Homologously collapsing stellar cores Astrophys. J. 238 991) with an adiabatic exponent γ = 4/3, to the (classical) Euler–Poisson equations without a cosmological constant, the self-similar (almost re-collapsing) time-periodic solutions with a negative cosmological constant (Λ < 0) are constructed. The solutions with time periodicity are novel. Based on these solutions, the time-periodic and almost re-collapsing model is conjectured in this paper, for some gaseous stars. Copyright © 2009 IOP Publishing Ltd.