- #1
Auburnman
- 11
- 0
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!