I solved it myself. The metric for lightlike separation implies g_{00}\dot{t}^2 +g_{11}\dot{r}^2+g_{22}\dot{\phi}^2 =0 and we have expressions for phi dot and t dot from the OP. Just plug them in and since the expression is true everywhere we evaluate it on the surface of the star i.e where...
Hi, I'm having trouble answering Question 9.20 in Hobson's book (Link: http://tinyurl.com/pjsymtd). This asks to prove that a photon will just graze the surface of a massive sphere if the impact parameter is b = r(\frac{r}{r-2\mu})^\frac{1}{2}
So far I have used the geodeisic equations...
Gravitational time dilation is already taken account of due to the 1/√g00 in the 4-velocity.
Yes, all I wanted was the 4 velocity of a particle relative to a distance observer that is thrown by a stationary observer at A with velocity u. I know it's a pretty useless expression in terms of...
I figured it out! Suppose we have an observer at infinity M, an observer A at co-ordinates (t,r) in M's frame and A pitches an object O at a 3-velocity u radially downwards as shown (file at bottom inconveniently).
In the frame of A the velocity of u is the distance radially traveled divided by...
Ok so I made some progress with the timelike geodeisic equation \dot{t} = \frac{k}{1-\frac{2\mu}{r}} equating k as equal to gamma at infinity.
This approach basically assumes you release a particle at infinity at some velocity that gives you gamma hence k and you then measure it again when it...
How do we calculate the 4 velocity of a particle that is projected radially downwards at velocity u at a radius ra?
The condition on 4 velocity is that gμνvμvν = 1 which implies that at radius ra we have
ga00(v0)2 + ga11(v1)2 = 1 (eq 1)
So if we start from xμ = (t,r) we get vμ = (1/√g00 ...