TITLE:
The Hawking Effect for Massive Particles
AUTHORS:
Bernard R. Durney
KEYWORDS:
Hawking Effect
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.4 No.1,
March
4,
2014
ABSTRACT: 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 k2 = 2e – 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
hasthe same value of e, andiscreated at equal
distances from the EH,(1– rin = rout – 1).Global
energy conservations force then the mass of the particle below the EH to be
negative, and equal to minus the mass the particle above the EH, i.e.,
the black hole looses energy as a consequence of pair production.