Transcript Black holes as Information Scramblers

FAR-FROM-EQUILIBRIUM ISOTROPISATION,
QUASI-NORMAL MODES AND RADIAL FLOW
Comparing numerical evolution with linearisation
Work with Michał Heller, David Mateos, Michał Spalinski, Diego Trancanelli and Miquel Triana
References: 1202.0981 (PRL 108) and 1210.xxxx
Wilke van der Schee
Supervisors: Gleb Arutyunov, Thomas Peitzmann,
Koenraad Schalm and Raimond Snellings
Workshop Holographic Thermalization, Leiden
October 11, 2012
Outline
2/19
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Simple set-up for anisotropy
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Quasi-normal modes and linearised evolution
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Radial flow (new results, pictures only)
Holographic context
3/19
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Simplest set-up:
 Pure
gravity in AdS5
 Background field theory is flat
 Translational- and SO(2)-invariant field theory
 We
keep anisotropy:
 Caveat: energy density is constant so final state is known
P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma (2008)
The geometry
4/19
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Symmetry allows metric to be:
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A, B, S are functions of r and t
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B measures anisotropy
Einstein’s equations simplify
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Null coordinates
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Attractive nature of horizon
Key differences with Chesler, Yaffe (2008) are
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Flat boundary
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Initial non-vacuum state
The close-limit approximation
5/19
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Early work of BH mergers in flat space
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Suggests perturbations of an horizon are always small
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 Linearise evolution around final state (planar-AdS-Schw):
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Evolution determined by single LDE:
R. H. Price and J. Pullin, Colliding black holes: The Close limit (1994)
Quasi-normal mode expansion
6/19
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Expansion:
Solution possible for discrete
Imaginary part
always positive
G.T. Horowitz and V.E. Hubeny, Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium(1999)
J. Friess, S. Gubser, G. Michalogiorgakis, and S. Pufu, Expanding plasmas and quasinormal modes of anti-de Sitter black holes (2006)
First results (Full/Linearized/QNM)
7
Bouncing off the boundary
8/19
IR,
9/19
normal,
UV
Statistics of 2000 profiles
10/19
Recent additions
11/19
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Same linearised calculations with a boost-invariant direction
 Subtlety: final state is not known initially
 Add-on: non-homogeneous and includes hydrodynamics
 Works well 
Second and third order corrections
 The expansion seems to converge
 Works quite well 
Radial flow
12/19
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Calculation incorporating longitudinal and radial expansion
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Numerical scheme very similar to colliding shock-waves:
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Assume boost-invariance on collision axis
Assume rotational symmetry (central collision)
 2+1D nested Einstein equations in AdS
P.M. Chesler and L.G. Yaffe, Holography and colliding gravitational shock waves in asymptotically AdS5 spacetime (2010)
Radial flow – initial conditions
13/19
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Two scales: T and size nucleus
Energy density is from Glauber model (~Gaussian)
 No momentum flow (start at t ~ 0.05fm/c)
 Scale solution such that T  506MeV at t  0.6fm/c
 Metric functions ~ vacuum AdS (not a solution with energy!)
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H. Niemi, G.S. Denicol, P. Huovinen, E. Molnár and D.H. Rischke, Influence of the shear viscosity of the quark-gluon plasma on elliptic flow (2011)
Radial flow – results
14/19
Radial flow - acceleration
15/19
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Velocity increases rapidly:
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Acceleration is roughly
 Small
1031 g
with R size nucleus
nucleus reaches maximum quickly
Radial flow – energy profile
16/19
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Energy spreads out:
Radial flow - hydrodynamics
17/19
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Thermalisation is quick, but viscosity contributes
Radial flow - discussion
18/19
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Radial velocity at thermalisation was basically unknown
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Initial condition is slightly ad-hoc, need more physics?
 We
get reasonable pressures
 Velocity increases consistently in other runs
 Results are intuitive
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Input welcome 
Conclusion
19/19
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Studied (fast!) isotropisation for over 2000 states
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Linearised approximation works unexpectedly well
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UV anisotropy can be large, but thermalises fast (though no bound)
Works even better for realistic and UV profiles
Numerical scheme provides excellent basis
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Radial flow, fluctuations, elliptic flow
What happens universally? What is the initial state?