Self-similar dynamics of a relativistically hot gas

摘要: In the presence of self-gravity, we investigate self-similar dynamics a relativistically hot gas with or without shocks in astrophysical processes stellar core collapse, formation compact objects, and supernova remnants central voids. The model system is taken to be spherically symmetric conservation specific entropy along streamlines adopted for relativistic whose energy-momentum relation expressed approximately by e = cP P being energy momentum particle c speed light. terms equation state, this leads polytropic index y 4/3. conventional κρ γ , where thermal pressure, p mass density, K global constant, included our theoretical framework. Two qualitatively different solution classes arise according values simple power-law scaling a, each which analysed separately systematically. With explicit conditions, all sonic critical lines appear straight. We obtain new asymptotic solutions that exist only Global various limits as well eigensolutions across are derived analytically numerically shocks. By streamlines, extend analysis Goldreich & Weber distribution variable time t radius r discuss consequences context homologous collapse prior supemovae. As an alternative rebound shock model, construct Einstein-de Sitter explosion connections outer flows including static part singular sphere. Under joint action pressure can also spherical voids sharp density variations their edges.