The nonlinear stage of evolution of spherically symmetric disturbances in an Einstein-de Sitter universe - Explosive and implosive modes

Details The nonlinear stage of evolution of spherically symmetric disturbances in an Einstein-de Sitter universe - Explosive and implosive modes The nonlinear stage of evolution of spherically symmetric disturbances in an Einstein-de Sitter universe - Explosive and implosive modes

Mar 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...270....1k&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 270, no. 1-2, p. 1-19.

Astronomy and Astrophysics

Astrophysics

2

Einstein Equations, Evolution (Development), Gas Dynamics, Gravitational Collapse, Shock Wave Interaction, Approximation, Nonlinear Equations, Space Density, Universe

Scientific paper

The evolution of a localized disturbance in an Einstein-de Sitter universe is considered in spherical approximation in Newtonian hydrodynamics. Two kinds of disturbances are distinguished: with positive or negative energy. If the adiabatic index gamma of an expanding matter is greater than a certain critical value gamma(c), both kinds of disturbances eventually grow to reach the final nonlinear state. If gamma is less than gamma(c), a positive energy disturbance absolutely decays, whereas the decay of a negative energy disturbance occurs for relatively small amplitude. For spherical geometry gamma(c) = 6/5, for cylindrical and plane geometries -7/6, and 10/9 respectively. The final state of a positive energy disturbance is a cosmological bubble which expands in a self-similar manner. The structure of a self-similar flow with a strong shock wave is found for the whole range gamma greater than 1 (the solutions for gamma less than 7/6 have not been known earlier). The solution for a shock wave of arbitrary amplitude is constructed for gamma = 6/5. The flow for a negative energy perturbation is not generally self-similar. The self-similar solutions exist for gamma = 6/5, and for a limited range of values of amplitudes.

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