- #1
latentcorpse
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An observer falls radially into a Schwarzschild black hole of mass [itex]M[/itex]. She starts from rest (i.e. [itex]\frac{dr}{d \tau} = 0[/itex]) at [itex]r = 10M[/itex]. How much time elapses on her clock before she hits the singularity?
Is my first step to take the metric equation
[itex]ds^2 = - ( 1 - \frac{2M}{r} ) dt^2 + \frac{dr^2}{(1 - \frac{2M}{r})} + r^2 ( d \theta^2 + \sin^2{\theta} d \phi^2 )[/itex]
and find the Euler Lagrange equations of motion?
Or is this barking up the wrong tree?
Is my first step to take the metric equation
[itex]ds^2 = - ( 1 - \frac{2M}{r} ) dt^2 + \frac{dr^2}{(1 - \frac{2M}{r})} + r^2 ( d \theta^2 + \sin^2{\theta} d \phi^2 )[/itex]
and find the Euler Lagrange equations of motion?
Or is this barking up the wrong tree?