1 Newtonian reference case

1000 mass bins, uniformly stacked, from 0 to 1, starting at m=0.001, so then we have m=0.002, 0.003, until m=1.

Initial condition:

r = (\frac{3m}{4πρ_{0}} )^{1/3} , β = 0.  (1)

\frac{dr}{dt} = β  (2)
\frac{dβ}{dt} = −\frac{m}{r^{2}}  (3)

Figure 1: Newtonian reference case for ρ_{0} = 1. Contours of constant radius, r = 0, 0.02, etc. The blue (red) contour corresponds to r = 0.1 (r = 0.2). Fixed time step δt = 5 × 10^{−5}.

2 TOV case

\frac{dβ}{dt} = −\frac{m}{|r(r − r_{G})|}.  (4)

3 TOV case with pseudorelativistic equation of motion

\frac{dr}{dt} = \frac{β}{\sqrt{1 + β^{2}}}  (5)

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Figure 2: Same as Fig. 1, but for TOV potential with r_{G} = 0.2.

Figure 3: Same as Fig. 2, but for the pseudorelativistic equation of motion.