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 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 dd t(S+A/4)= 2π F, with F the flux of the gravitational/matter radiation (integrated squared news tensor) emitted towards the future of the region.