Boundary description of planckian scattering in curved spacetimes

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 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.

Asymptotic perfect fluid dynamics as a consequence of AdS/CFT correspondence

“…The second example of an exact solution using our method is the geometry dual to a gauge theory shock-wave (on the boundary). Shockwave solutions have been constructed in AdS spaces [20,21] whose sources were in the bulk, or particles on the boundary [22].…”

Entropy production in collisions of gravitational shock waves and of heavy ions

“…where the second equality can be checked using (43). The last expression in (63) shows that, up to an overall prefactor, q is the square of the chordal distance between the point (x i , z)…”

“…Shock waves in anti-de Sitter spaceGravitational shock waves are well studied, both in R D−1,1 and AdS D : see for example[36,37,38,39,40,41,42,43,44,45]. The simplest of them can be constructed in two equivalent ways.…”

Off-center collisions in AdS5with applications to multiplicity estimates in heavy-ion collisions

“…If the impact parameter is not too large, then after the collision a black hole will probably form. To obtain a lower bound on the entropy of the black hole produced in such a collision, we use the method of [16], which was further developed in [17,18,19,38] and adapted to AdS space in [5,6,7,9,10,39,2,40]. The method is to find a marginally trapped surface S, composed of two parts: S = S + ∪ S − where the S i 's are parameterized by…”