Particle absorption by black holes and the generalized second law of thermodynamics

Abstract

The change in entropy, /DeltaS, associated with the quasi-static absorption of a particle of energy u by a Schwarzschild black hole (ScBH) is approximately (u/T)-s, where T is the Hawking temperature of the black hole and s is the entropy of the particle. Motivated by the statistical interpretation of entropy, it is proposed here that absorption should be suppressed, but not forbidden, when /DeltaS<0, which requires the absorption cross-section to be sensitive to /DeltaS. A purely thermodynamic formulation of the probability for absorption is obtained from the standard relationship between microstates and entropy. If /DeltaS>>1 and s<<u/T then the probability for the particle not to be absorbed is approximately exp[-u/T], which is identical to the probability for quantum mechanical reflection by the horizon of a ScBH. The manifestation of quantum behaviors in the new probability function may intimate a fundamental physical unity between thermodynamics and quantum mechanics.