News vs Information

Abstract

We consider the relative entropy between the vacuum state and a coherent state in linearized quantum gravity around a stationary black hole spacetime. Combining recent results by Casini et al. and Longo with the Raychaudhuri equation, the following result is obtained: Let $\mathfrak{A}$ be the algebra of observables assoiciated with a region that is the causal future of some compact set in the interior of the spacetime. Let $S$ be the relative entropy with respect to this algebra, $A$ the area of the horizon cross section defined by the region, computed to second order in the gravitational perturbation. If the region is time-translated by the Killing parameter $t$, then $\frac{d}{dt}(S+A/4)=2\pi F$, with $F$ the flux of the gravitational/matter radiation (integrated squared news tensor) emitted towards the future of the region.

11 pages, 1 figure. arXiv admin note: text overlap with arXiv:1903.07508, v2: some details added on function spaces and decay of solutions, refs. added

References in corpus (5)

• Notes on Some Entanglement Properties of Quantum Field Theory
• A c-theorem for the entanglement entropy
• Relative entropy for coherent states from Araki formula
• Comment on the Bekenstein bound
• Hadamard States From Light-like Hypersurfaces

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• Relative Entropy of Fermion Excitation States on the CAR Algebra
• Relative Entropy in de Sitter is a Noether Charge
• Entropy-area law and temperature of de Sitter horizons from modular theory
• From Quantum Relative Entropy to the Semiclassical Einstein Equations
• Notions of Fermionic Entropies of a Causal Fermion System
• Petz-Rényi relative entropy in QFT from modular theory
• A numerical analysis of Araki-Uhlmann relative entropy in Quantum Field Theory