Boundary description of Planckian scattering in curved spacetimes

TL;DR

This paper demonstrates that in the eikonal limit of gravity with a cosmological constant, the Einstein-Hilbert action simplifies to a boundary action describing shock-wave interactions, highlighting holographic aspects in curved spacetimes.

Contribution

It generalizes previous work by showing the boundary reduction of the Einstein-Hilbert action in any dimension with a cosmological constant, emphasizing the role of the off-diagonal Einstein action.

Findings

Boundary action describes shock-wave interactions up to collision point.

The reduction to boundary action is valid in any dimension with non-zero cosmological constant.

Connections to holography and existing AdS solutions are discussed.

Abstract

We show that for an eikonal limit of gravity in a space-time of any dimension with a non-vanishing cosmological constant, the Einstein -- Hilbert action reduces to a boundary action. This boundary action describes the interaction of shock-waves up to the point of evolution at which the forward light-cone of a collision meets the boundary of the space-time. The conclusions are quite general and in particular generalize the previous work of E. and H. Verlinde. The role of the off-diagonal Einstein action in removing the bulk part of the action is emphasised. We discuss the sense in which our result is a particular example of holography and also the relation of our solutions in $AdS$ to those of Horowitz and Itzhaki.