New Area Law in General Relativity

Abstract

We report a new area law in General Relativity. A future holographic screen is a hypersurface foliated by marginally trapped surfaces. We show that their area increases monotonically along the foliation. Future holographic screens can easily be found in collapsing stars and near a big crunch. Past holographic screens exist in any expanding universe and obey a similar theorem, yielding the first rigorous area law in big bang cosmology. Unlike event horizons, these objects can be identified at finite time and without reference to an asymptotic boundary. The Bousso bound is not used, but it naturally suggests a thermodynamic interpretation of our result.

Marginally trapped surfaces and AdS/CFT

“…Section 4 studies divergences in the area of the marginally trapped surfaces associated with the region near the AdS boundary and shows that, while the leading order divergences of our marginally trapped surfaces match those of the extremal surface, the subleading divergences generally differ. Section 5 then generalizes the thermodynamic results of [7,8] to holographic screens with non-compact leaves. We close with some brief discussion in section 6.…”

“…Holographic screens are also known as marginally trapped tubes [10], and are a generalization of dynamical horizons and future outer trapped horizons [11], removing the restriction [7] that the surface be spacelike. Since we focus on the boundary-anchored case, we also omit the usual requirement that the marginally trapped surfaces be compact.…”

“…Previous work has focused on generating them from null foliations (e.g. [7,8,12]), building the leaves of the holographic screen by finding a codimension-two surface with JHEP02(2018)049 Figure 1. A holographic screen can be constructed by null foliation from an observer's light cones.…”

“…Note that we may choose Σ 1I to be continuous in I. 7 We can also define the wedges associated to each of the surfaces of interest:…”

“…Such surfaces can be stitched together to form a continuous codimension-one surface, called a holographic screen, in which case the marginally trapped surfaces are called leaves of the screen. It was further shown in [7,8] that the leaves of the holographic screen obey a monotonic area law, and thus presumably a thermodynamic second law.…”