Second Law of Black Hole Mechanics for all 2d Dilaton Theories

TL;DR

This paper proves that all 2D dilaton gravity theories with matter obey a second law of black hole mechanics, ensuring entropy non-decrease under certain conditions, thus extending previous results to a broader class of theories.

Contribution

It generalizes the second law of black hole mechanics to all 2D dilaton theories with matter and arbitrary f(R) theories, under specific energy and stationarity conditions.

Findings

Entropy does not decrease if the null energy condition holds.

The second law applies to a wide class of 2D dilaton and f(R) theories.

The results extend previous proofs to more general theories.

Abstract

It is shown that all generalized two--dimensional dilaton theories with arbitrary matter content (with a curvature independent coupling to gravity) do not only obey a first law of black hole mechanics (which follows from Wald's general considerations, if the entropy S is defined appropriately), but also a second law: \delta S \ge 0 provided only that the null energy condition holds and that, loosely speaking, for late times a stationary state is assumed. Also any two-dimensional f(R)--theory is covered. This generalizes a previous proof of Frolov [1] to a much wider class of theories.