- #1
Romeo
- 13
- 0
Consider a model in which we let a body fall (radially) into a star, being the simplest example of the schwarzschild solution, in which the angular parts of the solution may be ignored, so that we consider:
[tex]
ds^2 = -(1- GM/r) dt^2 + (1- GM/r)^{-1}dr^2.
[/tex]
I have been told that this may be adapted to a Lagrangian of form:
[tex]
L(r, \dot{r}) = -(1- GM/r) (\frac{dt}{d\lambda})^2 + (1- GM/r)^{-1}(\frac{dr}{d\lambda})^2,
[/tex]
and then solved to find a general time for a body to 'fall' from rest, from a general distance R. How, I don't know (...I love supervisors).
I now have 13 books out upon general relativity, and am royally stuck. It is important that a solution avoids tensor calculus- i am aware that this is possible.
Any help with this would be incredibly appreciated.
Regards
Romeo.
[tex]
ds^2 = -(1- GM/r) dt^2 + (1- GM/r)^{-1}dr^2.
[/tex]
I have been told that this may be adapted to a Lagrangian of form:
[tex]
L(r, \dot{r}) = -(1- GM/r) (\frac{dt}{d\lambda})^2 + (1- GM/r)^{-1}(\frac{dr}{d\lambda})^2,
[/tex]
and then solved to find a general time for a body to 'fall' from rest, from a general distance R. How, I don't know (...I love supervisors).
I now have 13 books out upon general relativity, and am royally stuck. It is important that a solution avoids tensor calculus- i am aware that this is possible.
Any help with this would be incredibly appreciated.
Regards
Romeo.