Hello, I've enjoyed reading these forums for a while now as they have lots of great insight! Today I decided to register so I can ask a question that's been bothering me for a few days now. (By the way, I'm moving onto my senior year as a physics major)
So yea, to the question. I have been...
Light rays in the schwarzschild metric satisfy the differential equation
\frac {d^2u} {d\phi^2}+u=3Mu^2
u=1/r
I want to show that there is closed orbits with constant radius and also calculate the radius of the orbits as a function of the Schwarzschild radius.
Can anyone help...
Well, I think I finally figured out how to get good values for the local values of the Christoffel symbols (aka local gravitational accelerations) in the Schwarzschild metric. Some of the results are moderately interesting, though there is one point that still makes me wonder a bit.
If we...
What evidence is there that the schwarzschild metric is valid inside a black hole (as opposed to outside the Sun where evidence comes in the form of mercury's perihelion)?
Also, if a black hole is made from photons, would it be massless and move at
the speed of light?
The Schwarzschild Metric is only valid for R>2M, What are the units used here? Obviously R and M should have incompatible units...so how can any comparison of this type be made?
i'm toying around with the schwarzschild metric using it to find distances from a star in sphereical coordinates.
the metric is:
g** =
1/(1-2M/r) 0 0 0
0 r^2 0 0
0 0 r^2sin(theta)^2 0
0 0 0 -(1-2M/r)...