The Hawking Effect for Massive Particles

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This paper describes a particularly
transparent derivation of the Hawking effect for massive particles in black
holes. The calculations are performed with the help of Painlevé-Gullstrand’s
coordinates which are associated with a radially free-falling observer that
starts at rest from infinity. *It is shown that if the energy per unit
rest mass, e, is assumed to be related to the Killing constant, k, by* *k*^{2}* = *2*e –* 1* then
e, must be greater than ?*. For particles that are confined below the
event horizon (EH), *k* is negative.
In the quantum creation of particle pairs at the EH with *k* = 1, the
time component of the particle’s four velocity that lies below the EH is
compatible only with the time component of an outgoing particle above the
EH, *i.e*, the outside particle cannot fall back on the black hole.
Energy conservation requires that the particles inside, and outside the EH
has the same value of *e*, and is created at equal
distances from the EH, (1 – *r _{in}* =

References

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[2] Schutz, B. (2007) A First Course in General Relativity. Cambridge University Press, Cambridge.

[3] Carlip, S. (2004) Re: Hawking Radiation and Vacuum Fluctuation.
http://sci.techarchive.net/sci. physcsresearch/2004-10

[4] Wald, R.M. (2001) The Thermodynamics of Black Holes. Living Reviews Relativity, 4, 6.

[5] Parker, L. (1969) Quantized Fields and Particle Creation in expanding Universes. Physical Review, 183, 1057.