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

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.

Overspinning a black hole with a test body

It has long been known that a maximally spinning black hole cannot be overspun by tossing in a test body. Here we show that if instead the black hole starts out with below maximal spin, then indeed overspinning can be achieved. We find that requirements on the size and internal structure of the test body can be met if the body carries in orbital but not spin angular momentum. Our analysis neglects radiative and self-force effects, which may prevent the overspinning.