Spherically symmetric collapsing solution in the form of shadow wave

Key Points

• Stable shadow wave solutions were found even with unbounded density at the origin, suggesting unique behaviors in gravitational systems.
• The study introduces a density dependent viscosity term affecting momentum in the isothermal Euler-Poisson system, indicating significant physical implications.
• The findings extend to cases of vanishing pressure, highlighting the adaptability of the model for different astrophysical scenarios.
• Understanding these solutions is vital for advancing theories on star formation and gravitational collapse in astrophysics.