Revision history [back]

Velocity of time

Hi All,

I was looking at http://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Schwarzschild_geod.ipynb at the paragraph Computing numerical solutions/Timelike geodesics/Bounded orbit, at the following command:

params_values_bounded = {m:1, s_0:0, s_max:1500, t_0:0, r_0:8, th_0:pi/2, ph_0:1e-12,
Dt_0:sqrt(80.81)/(4*sqrt(3)), Dr_0:0, Dth_0:0, Dph_0:4.1/64}


I understand there are 4-coordinates (t,r,th,ph), and for each one there is a 2nd order Geodesic equation, so in total should be 8 initial conditions. How did you choose the value of Dt_0? How did you calculate this value? Is this the velocity of time at time zero. What is the physical significance of this value?

P.D. Did you notice there are no 3D figures in this Notebook?

Thanks,

Daniel