- #1
JohanL
- 158
- 0
[tex]
e^{-2 \lambda}(2r \lambda_r -1) + 1 = 8 \pi r^2G_\Phi(r,\mu)
[/tex]
[tex]
e^{-2 \lambda}(2r \mu_r +1) - 1 = 8 \pi r^2H_\Phi(r,\mu)
[/tex]
where
[tex]
G_\Phi(r,\mu) = \frac{2\pi}{r^2}\int_{1}^{\infty}\int_{0}^{r^2(\epsilon^2-1)} \Phi(e^{\mu(r)\epsilon,L}) \frac{\epsilon}{\sqrt{\epsilon^2-1-L/r^2}}dL
d\epsilon
[/tex]
[tex]
H_\Phi(r,\mu) = \frac{2\pi}{r^2}\int_{1}^{\infty}\int_{0}^{r^2(\epsilon^2-1)} \Phi(e^{\mu(r)\epsilon,L}) \frac{\epsilon}{\sqrt{\epsilon^2-1-L/r^2}}dL
d\epsilon
[/tex]
If you have a system like this and want to solve it numerically for [tex]\lambda [/tex] and [tex] \mu [/tex] how do you deal with the function [tex] \Phi [/tex]. I mean: It can be any function...i have never solved a system like that before.
thank you.
e^{-2 \lambda}(2r \lambda_r -1) + 1 = 8 \pi r^2G_\Phi(r,\mu)
[/tex]
[tex]
e^{-2 \lambda}(2r \mu_r +1) - 1 = 8 \pi r^2H_\Phi(r,\mu)
[/tex]
where
[tex]
G_\Phi(r,\mu) = \frac{2\pi}{r^2}\int_{1}^{\infty}\int_{0}^{r^2(\epsilon^2-1)} \Phi(e^{\mu(r)\epsilon,L}) \frac{\epsilon}{\sqrt{\epsilon^2-1-L/r^2}}dL
d\epsilon
[/tex]
[tex]
H_\Phi(r,\mu) = \frac{2\pi}{r^2}\int_{1}^{\infty}\int_{0}^{r^2(\epsilon^2-1)} \Phi(e^{\mu(r)\epsilon,L}) \frac{\epsilon}{\sqrt{\epsilon^2-1-L/r^2}}dL
d\epsilon
[/tex]
If you have a system like this and want to solve it numerically for [tex]\lambda [/tex] and [tex] \mu [/tex] how do you deal with the function [tex] \Phi [/tex]. I mean: It can be any function...i have never solved a system like that before.
thank you.