Weak Field Black Hole Formation in Asymptotically AdS Spacetimes

TL;DR

The paper investigates far-from-equilibrium thermalization in strongly coupled CFTs via the AdS/CFT correspondence by analyzing weak-field gravitational collapse in AdS and flat spacetimes under highly symmetric perturbations. It develops a controlled amplitude expansion around AdS, revealing that the exterior geometry is well described by a Vaidya metric at leading order, with horizon formation setting the boundary temperature and driving rapid, scale-dependent thermalization in local observables. A key finding is the distinction between instantaneous-like thermalization of local operators and slower relaxation of nonlocal observables, with a phase structure on spheres that exhibits sharp transitions (Choptuik-type) between plasma and glueball regimes. The work also introduces resummed perturbation theory to cure infrared divergences, analyzes both translationally invariant and spherically symmetric collapses, and provides phase diagrams showing when gravitational collapse yields black holes versus thermal gas, offering insights into rapid equilibration mechanisms in strongly coupled field theories and potential connections to real-world fast thermalization phenomena. The results have broad implications for understanding holographic thermalization, the role of dimensionality in equilibration dynamics, and the applicability of gravitational probes to far-from-equilibrium processes in strongly coupled systems.

Abstract

We use the AdS/CFT correspondence to study the thermalization of a strongly coupled conformal field theory that is forced out of its vacuum by a source that couples to a marginal operator. The source is taken to be of small amplitude and finite duration, but is otherwise an arbitrary function of time. When the field theory lives on $R^{d-1,1}$, the source sets up a translationally invariant wave in the dual gravitational description. This wave propagates radially inwards in $AdS_{d+1}$ space and collapses to form a black brane. Outside its horizon the bulk spacetime for this collapse process may systematically be constructed in an expansion in the amplitude of the source function, and takes the Vaidya form at leading order in the source amplitude. This solution is dual to a remarkably rapid and intriguingly scale dependent thermalization process in the field theory. When the field theory lives on a sphere the resultant wave either slowly scatters into a thermal gas (dual to a glueball type phase in the boundary theory) or rapidly collapses into a black hole (dual to a plasma type phase in the field theory) depending on the time scale and amplitude of the source function. The transition between these two behaviors is sharp and can be tuned to the Choptuik scaling solution in $R^{d,1}$.

Figures (6)

• Figure 1: Cross section of the causal diagram for the collapse process in an asymptotically global $AdS_{d+1}$ space. The conventional Penrose diagram for this process would include only the half of the diagram that to the right of its vertical axis of symmetry
• Figure 2: The 'Phase Diagram' for our dynamical stirring in global $AdS$. The final outcome is a large black hole for $x \ll \epsilon^\frac{2}{d}$ (below the dashed curve), a small black hole for $x\ll \epsilon^\frac{1}{d-1}$ (between the solid and dashed curve) and a thermal gas for $x \gg \epsilon^\frac{1}{d-1}$. The solid curve represents non analytic behaviour (a phase transition) while the dashed curve is a crossover.
• Figure 3: Numerical solution for dilaton to the leading order in amplitude at late time
• Figure 4: A plot of $\psi(\frac{1}{0.7}, y)$ as a function of $y$
• Figure 5: Numerical solution for the dilaton at late time in $d = 5$