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Posted by Bruce on March 19, 2001 23:22:47 UTC

We will stick to a Schwarzchild hole and make all units meters. You mentioned starting at zero at infinity. This is Newton's and Euler's paradigm. Relativity says
E=m
so the rest energy per unit rest mass at infinity (faraway in flat spacetime)
E/m=1
Lets say a neutrino and a particle with a nucleus both freely fall from faraway in flat spacetime and eventually interact at r. Lets say that the total kinetic energy of the freely falling particles of this interaction can be measured (this means physically measured AT the receiving station) at a receiving station at faraway in flat spacetime. It would be easier to say that the total kinetic energy of the interaction arrives at the receiving station faraway in flat spacetime as a pulse of light but you can think of it as daughter constituents comprised of the total kinetic energy of the interaction arriving at the receiving station.
According to SR the interactions total energy measured at r where the interaction takes place is
Eshell = m / (1-2M/r)1/2

Total kinetic energy at the interaction
Eflash = [m/(1-2M/r)1/2] - m

Measured kinetic energy at the receiving station faraway
Efaraway = Eflash(1-2M/r)1/2
Efaraway = m - m(1-2M/r)1/2

Also E/m = (1-2M/r)dt/dt = 1 is a constant of the motion.
when r = 2M (event horizon) the remote bookkeeper of GR calculates E/m = (1-2M/2M) = 0
The remote observer calculates the distance to the event horizon to be infinite. The local shell observer at the event horizon has a different perspective.

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