Relativistic free fall on a center.
1. Preliminaries : a constant force, F, acting on the particle.
The velocity tends to the limit, c :
2. The (unrealistic) newtonian free fall.
3. The relativistic free fall.
The center is fixed. The point is initially at rest a a distance r[0]=1 (M=10, =1, G=c=1, arbitrary units).
Position versus time :
Velocity versus time :