Deriving the hawking temperature

Reference no: EM13550460

Deriving the Hawking temperature T = (hbar)c^3/8(pi)kBGM rigorously from quantum field theory is beyond our scope. However, we can make its form plausible by the following considerations. Assume a particle– antiparticle pair having a rest mass m to be created near the event horizon of a spherical black hole. Use the uncertainty principle to estimate the separation Dr of the virtual pair after a time Dt permitted by the uncertainty principle, if the particle and antiparticle are assumed to separate at light velocity. Using Newtonian gravity, estimate the differential (tidal) gravitational force DF acting over this distance. Then, show that requiring the rest-mass energy E = mc2 to be comparable to DF ·Dr near the event horizon implies, up to constant factors

Reference no: EM13550460

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