Recent content by nocks

The model is of a photon's path around a black hole. The \pm is due to the fact that the photons distance from the black hole can increase and decrease in the same orbit. I've been advised to differentiate dr/d\lambda to get around the \pm but I am unsure as to how this will solve my problem...

hi there, I'm trying to plot r against \phi by solving the following ODEs using runge-kutta. The problem I'm having is with the square root. How do I know when it will be positive and when it will be negative? If this is a simple question I apologise I'm not that great with the maths :). E and...

wow it's been a while since I looked at this project. Thought i'd come back to it :) A few questions. Since I lack a good maths background, I would appreciate some advice on how I would implement these 3 equations into a numerical solver like Euler's or Runge-Kutta to get back some results that...

Having a bit of trouble with this but I have p as p = \frac{L^2(2M-r)}{2r^3}

Apologies for the lack of basic physics understanding but for a photon on approach what would it's angular momentum be?

That would be \frac{d^2r}{d\lambda^2} = - \frac{L^2(3M-r)}{r^4} Which gives me the closest radius for a stable orbit of a photon as 3M

Guess I should state that \frac{d}{dr}V^2(r) = \frac{2L^2M}{r^4} - \frac{2L^2(\left 1 - \frac{2M}{r} \right)}{r^3}

Given \left( \frac{dr}{d \lambda} \right)^2 &= E^2 - V^2(r) \right) and V^2(r) = \left(1 - \frac{2M}{r} \right)\frac{L^2}{r^2} I have \frac{d^2r}{d\lambda^2} = -\frac{1}{2}\frac{d}{dr}V^2(r)

I actually have the numerical recipes book next to me although I may avoid solving the elliptic integral https://www.physicsforums.com/showpost.php?p=2409536&postcount=7", and just use the approximation for light deflection, i.e. 4GM/bc^{2}, to get the einstein ring effect, and focus on the...

Could anyone expand on this please? I would appreciate the help. I have the the effective potential in the schwarzschild metric as (L being angular momentum) V_{eff} = ( 1 - \frac{r_{s}}{r})(mc^{2} + \frac{L^{2}}{mr^{2}}) Would this be enough information to solve for r and \Phi so that I...

what does W(r) define?

Given it's been a while since I've done any differentiation, is it simply: \frac{dr}{d \lambda} \right) &= \frac{ E - L}{W \left( r \right)}

Could you give me some more information on plotting the trajectory on a coordinate map? I've been toying with equations for a while now and not making much progress Thanks

Just an interest of mine. It's taking a while to get my head around the maths but I guess I'm slowly getting there.

Oh so the impact parameter is the distance parallel to the centre of the black hole at approach from infinty? Now to attempt plotting the trajectory. Is the equation I mentioned above enough for this? (i should mention I am not a physicist)