There are several ways to derive the geodesic equation. One of which is the variational method which I seemed to understand it because it was written in great details. Then it was mentioned …

May 22, 2016 · The geodesic equation used in general relativity is the following: $$ {d^2 x^\mu \over ds^2} =- \Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over ds}{d x^\beta \over ds}. $$ It …

Oct 31, 2021 · For an interesting discussion of this read the answers to What is the physical meaning of the affine parameter for null geodesic? However coordinate time is not an affine …

May 16, 2018 · $\begingroup$ @MichaelSeifert The text you linked is interesting, and seems to support my intuition that indeed the geodesic equation can be seen as a centripetal force …

Jul 7, 2016 · Planned maintenance impacting Stack Overflow and all Stack Exchange sites is scheduled for Wednesday, March 26, 2025, 13:30 UTC - 16:30 UTC (9:30am - 12:30pm ET).

Feb 12, 2024 · The Einstein field equations (EFE) are the EoM of the gravitational field, the geodesic equation describes the motion of free particles in curved spacetime. Your question is …

I need the following equation to be true, so i get the geodesics equations, but I don't know how one can say the following: $$ \int d\tau \,\delta g_{\mu\nu}\frac{dx^{\mu}}{d\tau} …

But, if every particle follows a geodesic in such an expanded spacetime, it may not be unreasonable to equate "particle" with "geodesic": to say that a particle is, per se, an aspect of …

Mar 30, 2019 · My project for obtaining my master's degree in computer science involved ray tracing in Schwarzschild spacetime in order to render images of black holes. These light rays …

Oct 5, 2019 · Christoffel symbols from Geodesic equation for a metric with non-diagonal elements. 2.