Why doesnt a photon escape from a black hole?

[stunner5000pt]

Explain why elight emitted at a point inside the Scwarzschild radius (r<a) cannot be seen by a distant observer. (by one at r-> infinity)
well we know the trajectory of a photon is given by


$$\dot{r}^2 = c^2 \lambda^2 - \left( 1 - \frac{a}{r}\right) \frac{J^2}{r^2}$$

where J repsents the angular momentum in units of mass
lambda is $$\lambda = \dot{t} \left( 1 - \frac{a}{r} \right)$$

so when r < a does the expression for r dot become imaginary? Is that what i am aiming to prove?

 

[dextercioby]

See the argument given by Dirac in its GR book when discussing black holes.

Daniel.