Thanks a lot to everyone, your answers made it way clearer than my old course notes!
I managed to put together a simple Runge-Kutta integrator and got meaningful trajectories. Made my day!
However it seems quite slow. I am doubting it is possible to have real-time raytraced rendering in a...
I think my code has the -+++ convention, if by that you mean the sign of the diagonal matrix elements of g.
Regardless of my choice of initial dx^0/ds the result of g_mn v^m v^n (sorry I cannot figure out how to put nice tex code) is negative, provided that the initial radial velocity and theta...
Thanks again! I used the spherical coordinates, and cooked up a quick s-step integrator which is probably wrong/inaccurate.
I'll do some more research to improve it.
Nevertheless I got somewhat reasonable.
https://www.dropbox.com/s/x1bilwwsk861iyj/GR.png?dl=0...
Thanks a lot! this is very helpful!
Just a few points are not clear, mostly because it has been ~10 years since my GR course (that I didn't fully understand anyway).
The whole high/low indexing confuses me a bit.
1) [ itex ] x^0 = t, x^1 = x, x^2=y, x^3=z [ /itex ]
I noticed the high indexes...
Hi, I'm Filippo, researcher in Aalto University.
I enjoy making numerical simulation methods.
Hope I can contribute here and find expert answers to my endless curiosity.
Cheers!
Hi,I'd like to build a simulation (realtime) of space ships near a black hole (neutral, still or rotating possibly). Key features would be:
1) the ships are test particles that do not affect the metric
a) possibly test rigid-bodies with GR consistent rotational DOF.
2) the ships can fire...