Can anybody explain to me why the calculation of the Schwarzschild radius:
R(sch) = (2GM/c^2)
is valid? I have trouble explaining why this should form the event horizon
because:
1. The equation can be derived purely from the one for escape velocity,
which is non-relativistic
2. The energy of a photon is a function of its "mass" rather than its
velocity, so why should an escape velocity be appropriate?
3. The escape velocity equation works 2 ways, so that an object falling
towards the black hole would be expected to accelerate to the escape
velocity (>c!)
Also, what happens to the energy of a photon emitted at the surface of a
black hole - if it is redshifted to infinite wavelength, its momentum (and
so "mass", and energy) is zero, which makes the gravitational potential
energy zero. Where has the starting energy gone?
Any explanation would be appreciated.
By the way, the argument on non-inertial frames has gone on long enough. The
effects seem to be agreed, but now the correspondance is just quibbling over
definitions. Sort it out!