General Relativity question involving Metrics

[Auburnman]

Homework Statement

(30 points) Consider the metric
ds^2 = -(1 -(r^2/R^2))dt^2 + (1-(r^2/R^2))^-1 dr^2 + (r^2)d(omega)^2

Note that spacetime becomes
at at small r, not large r. r < R.
(a) Calculate the (exact) gravitational redshift (w_2)/(w_1) between two stationary ob-
servers at radial coordinates r1 and r2 and the same angular coordinates.
Discuss interesting limiting cases.

(b) Calculate and sketch the effective potentials V (r) for the radial motion of particles,
for the cases of massive and massless particles.
Interpret this effective potential: are there stable orbits? Are particles attracted
to r = 0? Can particles reach r = 0?
(c) Draw some light cones. Comparing your plot to that for the Schwartzschild
metric, what appears to be happening at r = R?

Homework Equations

Schwartzchild metric, and the given metric

The Attempt at a Solution

for the first part i got (w2/w1) = [1-(r1^2/R^2)]^.5 / [1-(r2^2/R^2)]^.5 but i don't think this is correct please help!

 

[mrface]

I got the same thing for part (a). Number 4 is whack man!

 

[Auburnman]

you know how 2 do 4b? because if i get that i can get the rest of problem 4

 

[mrface]

I have an idea but haven't worked it out. The question just seems so vague that I'm not even sure if I'm on the right track. Is your curve for part (a) asymptotic?

 

[Auburnman]

yes, what did u get for the true false questions?

 

[mrface]

lol who is this?

 

[Auburnman]

does that matter?

 

[Auburnman]

is there some other median besides this that you would like to talk about the problems or u going to work on it alone?