Collapse of a self-gravitating Bose-Einstein condensate with attractive self-interaction

Understand

We study the collapse of a self-gravitating Bose-Einstein condensate with attractive self-interaction.

• Equilibrium states in which the gravitational attraction and the attraction due to the self-interaction are counterbalanced by the quantum pressure exist only below a maximum mass $M_{\rm max}=1.012\hbar/\sqrt{Gm|a_s|}$ where $a_s<0$ is the scattering length of the bosons and $m$ is their mass.
• For $M>M_{\rm max}$ the system is expected to collapse and form a black hole.
• We study the collapse dynamics by making a Gaussian ansatz for the wave function.