Information content of gravitational radiation and the vacuum

Known entropy bounds, and the generalized second law, were recently shown to imply bounds on the information arriving at future null infinity. We complete this derivation by including the contribution from gravitons. We test the bounds in classical settings with gravity and no matter. In Minkowski space, the bounds vanish on any subregion of the future boundary, independently of coordinate choices. More generally, the bounds vanish in regions where no gravitational radiation arrives. In regions that do contain Bondi news, the bounds are compatible with the presence of information, including the information stored in gravitational memory. All of our results are consistent with the equivalence principle, which states that empty Riemann-flat spacetime regions contain no classical information. We also discuss the possibility that Minkowski space has an infinite vacuum degeneracy labeled by a choice of Bondi coordinates (a classical parameter, if physical). We argue that this degeneracy cannot have any observational consequences if the equivalence principle holds. Our bounds are consistent with this conclusion.

Figure 1

Penrose diagram of an asymptotic flat spacetime. Gravitational radiation (i.e., Bondi news) arrives on a bounded portion of ${\mathcal{I}}^{+}$ (red). The asymptotic regions before and after this burst (blue) are Riemann flat. The equivalence principle requires that observers with access only to the flat regions cannot extract classical information; however, an observer with access to the Bondi news can receive information (see Sec. 3). We find in Sec. 4 that the asymptotic entropy bounds of Sec. 2 are consistent with these conclusions.

Figure 2

A short observation (green shaded rectangle) cannot distinguish the reduced graviton state from the vacuum reduced to the same region. The graviton delivers no information to this observer.

Figure 3

A long observation (green shaded rectangle) can distinguish the reduced graviton state from the reduced vacuum. The graviton carries information to this observer.

Figure 4

A graviton conveys $O(1)$ information as long as it has appreciable support in the region of observation.