Multi variable integration?
I am trying to integrate
where is a constant. I am trying to obtain an expression that can be plotted on a versus p chart.
Attempt at a solution:
My naive attempt was to simply integrate wrt p and I obtained
which then solves to
Unfortunately when plotted it seems unphysical, and I think I may have done the integration wrong. I suspect the problem is that the two variables p and are not independent and multivariable integration is required, but I have no experience of that and no idea where to start. Can anyone help? (Thinking)
References http://www.phys.au.dk/~fedorov/GTR/09/note11.pdf and Lemaitre metric - Wikipedia, the free encyclopedia
I am using the simplified version of the Lemaitre metric
which ignores angular motion and I am trying to obtain an expression for light paths which always have ds=0, so that for light:
and from the references
which I substituted into the dp/d equation to obtain the expression that I am trying to integrate. If it helps any, the value 2 can be substituted for . Any help would be greatly appreciated. (Smile)