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

Manwai Yuen

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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.


PACS

98.80.Es Observational cosmology (including Hubble constant, distance scale, cosmological constant, early Universe, etc)

95.30.Sf Relativity and gravitation

04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields

MSC

83F05 Cosmology

85A40 Cosmology (For relativistic cosmology, see 83F05)

Subjects

Gravitation and cosmology

Astrophysics and astroparticles

Dates

Issue 23 (7 December 2009)

Received 11 June 2009, in final form 31 July 2009

Published 6 November 2009



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