RECORD
On holographic thermalization and gravitational collapse of massless scalar fields
High Energy Physics - Theory · Submitted 7 Aug 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In all the cases our results indicate that such a strongly coupled system thermalizes in a typical time scale t_T=O(1)/T.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
In this paper we study thermalization in a strongly coupled system via AdS/CFT. Initially, the energy is injected into the system by turning on a spatially homogenous scalar source coupled to a marginal composite operator. The thermalization process is studied by numerically solving Einstein's equations coupled to a massless scalar field in the Poincare patch of AdS_5. We define a thermalization time t_T on the AdS side, which has an interpretation in terms of a spacelike Wilson loop <W(l =1/T)> in CFT. Here T is the thermal equilibrium temperature. We study both cases with the source turned on in short(Delta t <= 1/T) and long(Delta t >= 1/T) durations. In the former case, the thermalization time t_T = g_t/T <= 1/T and the coefficient g_t = 0.73 in the limit Delta t <= 0.02/T. In the latter case, we find double- and multiple-collapse solutions, which may be interpreted as the gravity duals of two- or multi-stage thermalization in CFT. In all the cases our results indicate that such a strongly coupled system thermalizes in a typical time scale t_T=O(1)/T.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we study thermalization in a strongly coupled system via AdS/CFT. | contribution 0.96 | 0.86 | 0.04 | asserted 0.76 |
| s1 | Initially, the energy is injected into the system by turning on a spatially homogenous scalar source coupled to a marginal composite operator. | method 0.96 | 0.75 | 0.02 | asserted 0.99 |
| s2 | The thermalization process is studied by numerically solving Einstein's equations coupled to a massless scalar field in the Poincare patch of AdS_5. | method 1.00 | 0.92 | 0.03 | asserted 0.98 |
| s3 | We define a thermalization time t_T on the AdS side, which has an interpretation in terms of a spacelike Wilson loop <W(l =1/T)> in CFT. | contribution 0.55 | 0.90 | 0.06 | asserted 0.99 |
| s4 | Here T is the thermal equilibrium temperature. | interpretation 0.47 | 0.16 | 0.02 | asserted 0.97 |
| s5 | We study both cases with the source turned on in short(Delta t <= 1/T) and long(Delta t >= 1/T) durations. | method 0.60 | 0.89 | 0.03 | asserted 0.97 |
| s6 | In the former case, the thermalization time t_T = g_t/T <= 1/T and the coefficient g_t = 0.73 in the limit Delta t <= 0.02/T. | result 1.00 | 0.96 | 0.10 | asserted 1.00 |
| s7 | In the latter case, we find double- and multiple-collapse solutions, which may be interpreted as the gravity duals of two- or multi-stage thermalization in CFT. | interpretation 0.51 | 0.96 | 0.09 | hedged possibility 0.83 |
| s8 | In all the cases our results indicate that such a strongly coupled system thermalizes in a typical time scale t_T=O(1)/T. | result 0.94 | 0.94 | 0.78 | hedged possibility 0.94 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
In this paper we study thermalization in a strongly coupled system via AdS/CFT. Initially, the energy is injected into the system by turning on a spatially homogenous scalar source coupled to a marginal composite operator. The thermalization process is studied by numerically solving Einstein's equations coupled to a massless scalar field in the Poincare patch of AdS_5. We define a thermalization time t_T on the AdS side, which has an interpretation in terms of a spacelike Wilson loop <W(l =1/T)> in CFT. Here T is the thermal equilibrium temperature. We study both cases with the source turned on in short(Delta t <= 1/T) and long(Delta t >= 1/T) durations. In the former case, the thermalization time t_T = g_t/T <= 1/T and the coefficient g_t = 0.73 in the limit Delta t <= 0.02/T. In the latter case, we find double- and multiple-collapse solutions, which may be interpreted as the gravity duals of two- or multi-stage thermalization in CFT. In all the cases our results indicate that such a strongly coupled system thermalizes in a typical time scale t_T=O(1)/T.
Human review
References
How the literature uses it
29 arXiv papers cite this in 48 sentences
Papers citing it · 21 sentences without a confident label
Uses its method or tool 4 papers
-
([ref]) can be solved by the numerical scheme described in detail in Ref. [ref] : Given $f$, $δ$, $V$ and $P$ at $t = t_j$, we first calculate $V$, $P$ and $f$ at the next time step $t_j+1$ by solving ([ref]), ([ref]) and ([ref]).
On holographic thermalization and gravitational collapse of tachyonic scalar fields · Numerical scheme · 1.00
-
We consider a model of dynamical holographic thermalization [ref] which has been recently used to study thermalization time scale of strongly coupled plasmas.
Quantum corrections to dynamical holographic thermalization: entanglement entropy and other non-local observables · Introduction and motivation · 0.80
-
We then have used the third order Adams-Bashforth method for time-marching and finite difference in the spatial part [ref] , denoting by $dt$ the time intervals and by $du$ the space intervals.
Gravitational collapse in the AdS background and the black hole formation · Initial and boundary conditions and the solution algorithm · 1.00
Compares with it 4 papers
-
In order to compare with the results of the massless scalar in Ref. [ref] we take $g_t$ as a function of $Δt T$.
On holographic thermalization and gravitational collapse of tachyonic scalar fields · The thermalization time · 0.97
-
Our results agree with those presented in [ref] .
Gravitational collapse in the AdS background and the black hole formation · Energy and mass behavior · 0.97
-
In contrast to [ref] where a small cutoff close to the boundary is used to avoid the singularity in eq [ref], we have redefined $A(z,t)=zÃ(z,t)$.
Gravitational infall in the hard wall model · Introduction · 0.91
Cites it as support 2 papers
-
The thermalization time scale is typically fast for the Vaidya-AdS metric [ref] , and hence it would be suitable to focus on the effect of rapid thermalization.
Dynamical Meson Melting in Holography · Setup · 0.96
-
However, our holographic construction, as well as holographic studies of quantum quenches, [ref] , demonstrates that the out-of-equilibrium character of certain microstates is manifest at the macroscopic level.
Holographic second laws of black hole thermodynamics · Lessons for general black holes? · 0.98
Cites it as background 12 papers
-
The use of this prescription to study the thermalization following the quenches in various Vaidya-like backgrounds can be found in [ref] .
Holographic approach to thermalization in general anisotropic theories · Introduction · 0.83
-
The thermalization of a spatially homogeneous system initially in a non-equilibrium state created by a marginal perturbation has been studied both perturbatively [ref] and numerically [ref] .
On holographic thermalization and gravitational collapse of tachyonic scalar fields · Introduction · 0.93
-
So far, the studies [ref] - [ref] have considered the evolution of an AdS-Vaidya thin shell, even though at the moment it is not known how to get the initial Vaidya shell condition from a QFT evolution.
Dynamics of holographic thermalization · Introduction and motivation · 0.80
What it cites · 19 sentences without a confident label
Uses the method or tool of 5 papers
-
We will deal with more general cases using a numerical method similar to that used in the global patch of $AdS_d+1$ [ref] .
On Field Theory Thermalization from Gravitational Collapse · Introduction · 0.99
-
We will deal with more general cases using a numerical method similar to that used in the global patch of $AdS_d+1$ [ref] .
On weakly turbulent instability of anti-de Sitter space · Introduction · 0.99
-
We will deal with more general cases using a numerical method similar to that used in the global patch of $AdS_d+1$ [ref] .
Rapid Thermalization in Field Theory from Gravitational Collapse · Introduction · 0.99
Compares with 2 papers
-
Note that the thermalization time $t_T$ is physically different from the coordinate-dependent formation time of the black brane $t_BH∼Δt$ in ingoing Eddington-Finkelstein coordinates reported in Ref. [ref] .
Weak Field Black Hole Formation in Asymptotically AdS Spacetimes · Narrow waves$(Δt = 1√(a) ≲1T)$: $ϵa≲1$ · 0.83
-
This is in sharp contrast with bottom-up thermalization in perturbative QCD [ref] , in which soft gluons equilibrate more quickly than hard gluons.
Thermalization in Weakly Coupled Nonabelian Plasmas · Introduction · 1.00
Cites as support 1 paper
-
Those high $ω$ modes split into low $ω$ modes very rapidly [ref] .
Jet evolution in the N=4 SYM plasma at strong coupling · Introduction · 0.98
Cites as background 26 papers
-
For this kind of initial conditions, the interested reader is referred to [ref] for boost-invariant cases and [ref] for the global patch of $AdS_d+1$.
A comment on AdS collapse of a scalar field in higher dimensions · Introduction · 0.89
-
For this kind of initial conditions, the interested reader is referred to [ref] for boost-invariant cases and [ref] for the global patch of $AdS_d+1$.
On Field Theory Thermalization from Gravitational Collapse · Introduction · 0.89
-
For this kind of initial conditions, the interested reader is referred to [ref] for boost-invariant cases and [ref] for the global patch of $AdS_d+1$.
Simulation of Asymptotically AdS5 Spacetimes with a Generalized Harmonic Evolution Scheme · Introduction · 0.89
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.