# News vs Information

## TL;DR

This paper derives a relation connecting the change in relative entropy and horizon area in linearized quantum gravity around black holes, linking it to gravitational radiation flux via the news tensor.

## Contribution

It establishes a novel formula relating the rate of change of relative entropy and horizon area to gravitational radiation flux in a black hole spacetime.

## Key findings

- Derived a formula connecting entropy change and horizon area to gravitational flux.
- Linked quantum information measures to classical gravitational radiation.
- Extended previous results by combining quantum field theory and gravitational dynamics.

## 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 $\frak A$ 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 $\frac{d}{d t}(S+A/4)= 2\pi F$, with $F$ the flux of the gravitational/matter radiation (integrated squared news tensor) emitted towards the future of the region.