Abstract
In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole mechanics extends to higher derivative theories via the Noether charge construction of Wald. One also expects the statement of the second law, which in Einstein-Hilbert theory owes to Hawking’s area theorem, to extend to higher derivative theories. To argue for this however one needs a notion of entropy for dynamical black holes, which the Noether charge construction does not provide. We propose such an entropy function for the family of Lovelock theories, treating the higher derivative terms as perturbations to the Einstein-Hilbert theory. Working around a dynamical black hole solution, and making no assumptions about the amplitude of departure from equilibrium, we construct a candidate entropy functional valid to all orders in the low energy effective field theory. This entropy functional satisfies a second law, modulo a certain subtle boundary term, which deserves further investigation in non-spherically symmetric situations.
Highlights
The precise form of the higher derivative corrections depend on the nature of the UV completion
In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects
The laws of black hole mechanics can be interpreted as laws of thermodynamics
Summary
The precise form of the higher derivative corrections depend on the nature of the UV completion. Wald argued that for stationary black hole solutions of higher derivative gravity theories, the entropy is a Noether charge associated with time translations along the horizon generating Killing field. This Wald entropy was constructed to explicitly satisfy the first law of thermodynamics, which being an equilibrium statement, can be understood in the stationary solution. In its crudest version it says that, in a physical process in which a system evolves from one equilibrium configuration to another, the total entropy must increase Whilst this is a non-local statement, comparing only the initial and final configurations, one can ensure this by exhibiting a function of the system variables, the entropy function, which is monotone under time evolution, and reduces in equilibrium to the familiar notion of entropy. These requirements, per se, seem quite unrestrictive, for we make no demand of uniqueness
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