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

Abstract

The change in entropy, Δ S , associated with the quasi-static absorption of a particle of energy ε by a Schwarzschild black hole (ScBH) is approximately ( ε / 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 the absorption should be suppressed, but not forbidden, when Δ S <0, which requires the absorption cross section to be sensitive to Δ S . A purely thermodynamic formulation of the probability for the absorption is obtained from the standard relationship between microstates and entropy. If Δ S ≫1 and s ≪ ε / T , then the probability for the particle not to be absorbed is approximately exp[− ε / T ], which is identical to the probability for quantum mechanical reflection by the horizon of an ScBH. The manifestation of quantum behaviours in the new probability function may intimate a fundamental physical unity between thermodynamics and quantum mechanics.