I see where you are going with that. I tried something like that, but using
ds' - cd\tau' = \lambda (ds - cd\tau) and
ds' + c d\tau' = \mu (ds + cd\tau)
I then did the usual algebra to get Lorentz type transformations. By defining a four-velocity u as \frac{ds}{d\tau} which is defined as...
Sorry, that I took a hiatus. I was reading to get a handle on my question. Okay, the general idea is that general relativity gives us ds^2 = g_{ij} dx^1 dx^j where g is the spacetime metric. If within the metric we set m=0, or r -> infty, then we get the flat spacetime which gives the gamma from...
That is pretty much what I am talking about, but in the vicinity of a black hole. I was looking at the explanation for the Lorentz velocity transformations and played around with trying to get an equation for the gravity field using dtau. I was hoping someone had an idea of how to start using...
Sorry typed the wrong sign in the denominator. But the point is how to calculate the relative velocity in a gravity well (i.e. near big astrophysical body). The equation for SR is found everywhere, but how do we derive the relation for GR? The equations for SR are in a flat spacetime. How do we...
I know about the addition of velocities for SR v = (v1+v2)/(1-v1*v2/c^2). This equations is derived using Lorentz transformations. How do I derive the addition of velocity formula for particles in a non-inertial frame? Can I just add gammas? u = (u1+u2)/(1-u1*u2/u0^2)
where
u1 = gamma*v1
u2 =...