Recent content by Tachytaenius

By derive the basis vectors from the metric tensor I mean: acquire a formula to calculate the values of the basis vectors, at any point on the manifold, using the metric tensor. In my current mental model, the "starting point" is to choose coordinates (and define anywhere they wrap around) and...

As I understand from my self-study (and I'm well aware I may be wrong, so please correct me and/or point me in the right direction etc if so), the metric tensor is more or less what describes the shape of a manifold. It's the fundamental object from which most things tend to be derived from...

Given that the Wikipedia page for the Ellis wormhole has some questionable claims about circular geodesics of constant rho which, on its talk page, have been contested... I'm beginning to wonder if the geodesics that turn around are at all accurate. I feel like I would never've predicted them...

Turns out, with enough precise configuration, my code is able to get geodesics that spiral into and out of the wormhole throat already. But I still can't work out the geodesics that come towards and then just turn away.

@Ibix I returned to working on this, and-- assuming you're okay with the ping-- I have a more specific question to ask about the differing null geodesics and the possibility you mentioned that the exclusion of time is the problem. Do, in general, null geodesics through static spacetimes (like...

I tried the simulation with the equations mentioned for velocity, but the results did not seem to match either my or their geodesics. Would parallel transport of the forward vector, which relies on Christoffels in my case, work differently? I tried to modify the acceleration equations you...

I might be being silly but it doesn't look like I can edit my post anymore. I was just going to fix that ρ²=(r²+b²), not ρ.

Thank you for the reply! Would timelike and null geodesics even look different in a spacetime that doesn't change with time? For the Euler integrator, I actually changed it to a general system where both Euler and Runge-Kutta 4 can be specified, along with a number of steps (you can see it in...

I managed to figure out an issue with the geodesics I move with not matching the geodesics shown in the visualisation; that was just numerical error. Fixed it by calculating the basis vectors analytically rather than numerically. For the remaining issue: my current lead for the entirely...

Hi, what I thought I'd managed to do some months ago was to create a 2D manifold movement simulation / visualisation on a catenoid, to make a traversable [cross section of an] Ellis wormhole. I have noticed, though, that the geodesics on the Wikipedia page for the Ellis wormhole don't really...