| 68 | |

| 69 | I used mathematica to numerically solve the equation of motion for a uniform sphere as given in Carroll and Ostlie, and checked the solution was correct against a result they published in that book. For the 1/50 case, the function R(t) looks like, |

| 70 | |

| 71 | |

| 72 | rho(t) looks like |

| 73 | |

| 74 | |

| 75 | Here you see that the R(t) drops to zero at the freefall time. You see the density diverging at this point, given the unphysical condition r=0. The collapse accelerates in time, becomming faster and faster by the end. The density increases everywhere uniformly, and is only a function of time. |

| 76 | |

| 77 | For all the plots I made, the simulation time was less than the freefall time of the ambient. Additionally, R(t) never fell inside of the BE sphere. |

| 78 | |

| 79 | Here are the results, |