Larson–Penston Self-similar Gravitational Collapse
Yan Guo, Mahir Hadžić, Juhi Jang
Abstract
Abstract Using numerical integration, in 1969 Penston (Mon Not R Astr Soc 144:425–448, 1969) and Larson (Mon Not R Astr Soc 145:271–295, 1969) independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state $$p=k\varrho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mi>k</mml:mi><mml:mi>ϱ</mml:mi></mml:mrow></mml:math> , $$k>0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>k</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> , and subject to Newtonian gravity. We rigorously prove the existence of such a Larson–Penston solution.