Black hole thermodynamics at null infinity. Part 1: Dual Generalized Second Law

TL;DR

This paper formulates a dual version of the generalized second law of black hole thermodynamics from the perspective of observers at null infinity, using algebraic quantum field theory to identify a new thermodynamic potential that governs irreversible evolution.

Contribution

It introduces a dual GSL at null infinity based on asymptotic observables, extending the traditional horizon-based GSL with a new thermodynamic potential.

Findings

A dual GSL involving a thermodynamic potential at null infinity.

Different vacuum states lead to free energy or grand potential forms.

The dual GSL complements the standard GSL involving horizon area.

Abstract

The generalized second law (GSL) of black hole thermodynamics asserts the monotonic increase of the generalized entropy combining the black hole area and the entropy of quantum fields outside the horizon. Modern proofs of the GSL rely on information theoretic methods and are typically formulated using algebras of observables defined on the event horizon together with a vacuum state invariant under horizon symmetries, inducing a geometric modular flow. In this work, we formulate a dual version of the generalized second law from the perspective of asymptotic observers at future null infinity, who do not have access to the black hole area. Our approach exploits the dependence of the second law on the choice of algebra of observables and of a reference state invariant under suitable symmetries, in close analogy with open quantum thermodynamics. Using algebraic quantum field theory and modular theory, we analyze several physically motivated vacuum states, including the Hartle Hawking state and two classes of regularized vacua. We show that, at null infinity, the monotonic quantity governing an irreversible evolution is no longer the generalized entropy, but rather a thermodynamic potential constructed from asymptotic observables. Depending on the chosen vacuum, this potential takes the form of the free energy or of a generalized grand potential built from the Bondi mass and additional (angular) mode dependent chemical potentials. The resulting inequalities define a dual generalized second law at future null infinity, which can be consistently combined with the standard GSL involving variations of the black hole area.