Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976phrvd..13.2188h&link_type=abstract
Physical Review D - Particles and Fields, 3rd Series, vol. 13, Apr. 15, 1976, p. 2188-2203.
Astronomy and Astrophysics
Astronomy
453
Black Holes (Astronomy), Particle Emission, Quantum Mechanics, Radiance, Astronomical Models, Scalars, Schwarzschild Metric, Singularity (Mathematics)
Scientific paper
The Feynman path-integral method is applied to the quantum mechanics of a scalar particle moving in the background geometry of a Schwarzschild black hole. The amplitude for the black hole to emit a scalar particle in a particular mode is expressed as a sum over paths connecting the future singularity and infinity. By analytic continuation in the complexified Schwarzschild space, this amplitude is related to that for a particle to propagate from the past singularity to infinity and, by time reversal, to the amplitude for the black hole to absorb a particle in the same mode. The form of the connection between the emission and absorption probabilities shows that a Schwarzschild black hole will emit scalar particles with a thermal spectrum characterized by a temperature which is related to its mass. A conceptually simple derivation of black-hole radiance is obtained. The extension of this result to other spin fields and other black-hole geometries is discussed.
Hartle James B.
Hawking Stephen W.
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