Recent content by LazyPhysicist1

Got it, I solved for the coefficents. One last thing; do I take b as the impact parameter rsin(theta) from the nongravitational case, or ##b=\frac{r^2 \sin ^2 \theta}{1-\frac{2 M}{r}} \frac{d \phi}{d t}##, which is the impact parameter in schwarzachild spacetime. Also, I take it to be the...

Could you be a little more specific as to how I would determine D given initial photon direction angle a/initial gradient of light ray? I already incorporated angle a into the impact parameter.

How do I solve for D?

Got it! Thanks a lot!

Thank you! I get ##\epsilon = \frac{\cos{2\phi}+3}{2b} + c(\sin{\phi} + \cos{\phi})## thus giving me a solution of ##u(\phi) = \frac{(\frac{\cos{\phi}+3}{2b} + c(\sin{\phi} + \cos{\phi}) + \sin{\phi})}{b}##, where ##b=\frac{r^2 \sin ^2 \theta}{1-\frac{2 M}{r}} \frac{d \phi}{d t}## How do I...

Using the null geodesic and the Schwarzschild metric, this differential equation for photon trajectory near a mass can be derived, where u is r_s /2r: Though this nonlinear ode is fairly easy to approximate (which I already have), I'm looking for an analytic solution or an approximate...