The Einstein field equations are 10 in number and they describe the dynamics of a spatial surface, and its conjugate momentum metric, for a total of 6 variables. The coordinate fixing condition, analogous to a gauge condition, are 4 additional equations that fix the initial spatial surface.
This is different from geodesics, which correspond to the geodesic motion or separation of two masses. LC On Tuesday, August 4, 2020 at 2:13:10 PM UTC-5 agrays...@gmail.com wrote: > Maybe this will clear things up. EE has 10 independent equations, so one > needs 10 initial conditions to define the path of a test particle in > spacetime. What are they, and what would distinguish a geodesic from a > non-geodesic solution? TIA, AG > > > On Tuesday, August 4, 2020 at 12:29:26 PM UTC-6, Brent wrote: >> >> You can choose coordinates so that a particular geodesic is a coordinate >> axis. >> >> Brent >> >> On 8/4/2020 3:24 AM, Lawrence Crowell wrote: >> > What bothers me about this is that the spatial coordinates generally >> > depend on each other, and time. In this situation will the geodesic >> > equations yield a solution where the spatial coordinates remain fixed? >> AG >> >> -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/d5007d72-2086-4fc7-a1ed-2e6b3eb6ae35n%40googlegroups.com.
