Mathematics – Probability
Scientific paper
Sep 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975phrvd..12.1519p&link_type=abstract
Physical Review D - Particles and Fields, 3rd Series, vol. 12, Sept. 15, 1975, p. 1519-1525.
Mathematics
Probability
72
Black Holes (Astronomy), Particle Production, Probability Distribution Functions, Thermal Radiation, Black Body Radiation, Gravitation Theory, Gravitational Collapse, Particle Density (Concentration), Wave Functions
Scientific paper
It has been established by Hawking (1975) that a spherical black hole formed by collapse creates particles and that the average number of outgoing particles created in each mode obeys a thermal distribution law. The present paper outlines a simple and straightforward derivation of the blackbody probability distribution of the emitted particles. This is accomplished by calculating the matrix elements in the expansion of the initial vacuum state in terms of the basis of the late-time Fock space, in the approximation where backscattering by the static exterior Schwarzschild spacetime is neglected. The derived particle number distribution is shown to correspond to thermal radiation. Two key equations are obtained, and the consistency of the various orthonormality and commutation relations is verified.
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