Critical formation of trapped surfaces in the collision of gravitational shock waves

Abstract

We study the formation of marginally trapped surfaces in the head-on collision of two shock waves both in anti-de Sitter and Minkowski space-time in various dimensions as a function of the spread of the energy density in transverse space. For D = 4 and D = 5 it is shown that there exists a critical value of this spread above which no solution to the trapped surface equation is found. In four dimensions the trapped surface at criticality has a finite size, whereas in five the critical size vanishes. In both cases we find scaling relations characterized by critical exponents. Finally, when D > 5 there is always a solution to the trapped surface equation for any transverse spread.

Holographic phase diagram of quark-gluon plasma formed in heavy-ion collisions

“…Alvarez-Gaume et al considered the central collision of shock waves sourced by a nontrivial matter distribution in the transverse space and found a critical phenomenon occurring as the shock wave reaches some dilution limit [31]. This criticality may be related to the criticality found in [29], where the numerical results show the existence of a simple scaling relation between the critical impact parameter and the energy of colliding waves.…”

Jet quenching and holographic thermalization with a chemical potential

“…The issue was studied by implementing various approaches in the literature. In [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] the collisions of gravitational shock waves are introduced to mimic the colliding nuclei in the relativistic collisions. In [24,25] time-dependent and boost-invariant metrics, associated with the plasma undergoing Bjorken expansion, were investigated and further generalized in [26] with a chemical potential.…”

Colliding AdS gravitational shock waves in various dimensions and holography

“…Indeed, applying the holographic prescription [9] to the solution found in [14] for the wave profile Φ(z, x), the associated holographic energy-momentum tensor is 3) and similarly for T vv CFT by replacing u → v. Thus no trace of the smearing of the gravitational source is left in the energy distribution in the boundary theory, its transverse size being determined solely by the value of the holographic coordinate of the source, z = L.…”

“…[14] the formation of trapped surfaces in the head-on collision of two shock waves was studied for incoming waves characterized by a finite size in transverse space, in contrast with the case studied in [4] where the energy density along the wave-front follows a deltafunction distribution in transverse coordinates. For D = 4 and D = 5 it was found that the marginally closed trapped surface only forms if the transverse size of the wave is smaller than certain critical value.…”

“…If we interpret the formation of the trapped surface as a signal of eventual black hole formation as a result of the collision, this could imply at face value the existence of a threshold for thermalization in the holographic gauge theory as a function of the spread of the wave in the gravitational dual. It is not clear, however, what meaning the spread of the gravitational sources introduced in [14] might have in the holographic conformal field theory.…”