Weak field black hole formation in asymptotically AdS spacetimes

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 .

Rapid thermalization in field theory from gravitational collapse

“…The thin Vaidya shell approximation -Of the many setups discussed in the literature, the one that can be most directly compared to our work here is the one presented in [18]. This work provided, to our knowledge, the first systematic analysis of the thin shell Vaidya collapse as the dual of rapid thermalization in field theory.…”

“…We go beyond previous attempts within the AdS/CFT approach that relied on perturbation theory [18] or toy models for quench [19][20][21]. Our focus is on properties of the thermalization time.…”

“…Local gauge-invariant operators are mostly sensitive to geometry near the boundary. As explained in [18], in the large N limit which is the region explored by the gauge/gravity correspondence, trace factorization ensures that the expectation value of products equals the product of expectation values. Only one-point functions of gauge invariant operators survive.…”

“…In particular, we denote by t AH the coordinate time t at which an apparent horizon first forms. Note that our coordinate t has geometric meaning in that it is the coordinate that is orthogonal to the area coordinate r. However, one might also want to know how long the process takes in terms of an ingoing null coordinate v as used in [18]. Such a coordinate is constant along ingoing null geodesics and can be normalized by e.g.…”

Jet quenching and holographic thermalization with a chemical potential

“…We also note that the background metric generated by a time-varying weak dilaton field produces AdS-Vaidya-type background [34] and provides a very good quantitative approximation in the thin-shell limit. In [42][43][44], various non-local operators have been studied in the AdS-Vaidya spacetime to probe aspects of thermalization of the medium; and generalized in the presence of a charged shell where the spacetime is represented by AdS-RN-Vaidya metric [45,46].…”