Challenging the generalized second law

TL;DR

This paper investigates the conditions under which the generalized second law of black hole thermodynamics holds, analyzing classical and quantum effects that protect or violate the law in various black hole scenarios.

Contribution

It identifies specific classical and quantum effects that uphold or threaten the GSL in different black hole configurations, extending understanding of the law's robustness.

Findings

Classical backreaction effects protect the area theorem in near-extremal black holes.

Charge-induced repulsion effects prevent GSL violations in certain scenarios.

Quantum buoyancy may safeguard the GSL when the fine structure constant exceeds unity.

Abstract

The generalized second law (GSL) of black hole thermodynamics states that the sum of changes in black hole entropy and the ordinary entropy of matter and fields outside the hole must be non-negative. In the classical limit, the GSL reduces to Hawking's area theorem. Neither law identifies the specific effects which makes it work in particular situations. Motivated by Davies' recent gedanken experiment he used to infer a bound on the size of the fine structure constant from the GSL, we study a series of variants in which an electric test charge is lowered to a finite radius and then dropped into a Schwarzschild, a near-extremal magnetic Reissner-Nordstrom or a near-extremal Kerr black hole. For a classical charge, we demonstrate that a specific "backreaction" effect is responsible for protecting the area theorem in the near-extremal examples. For the magnetically charged Reissner-Nordstrom hole an area theorem violation is defused by taking into account a subtle source of repulsion of the charge: the spinning up of the black hole in the process of bringing the charge down to its dropping point. In Kerr hole case, the electric self-force on the charge is sufficient to right matters. However, in all experiments involving an elementary charge, the full GSL would apparently be violated were the fine structure constant greater than about order unity. We argue that in this case a quantum effect, the Unruh-Wald quantum buoyancy, may protect the GSL.