Thermalization of Wightman functions in AdS/CFT and quasinormal modes

Abstract

We study the time evolution of Wightman two-point functions of scalar fields in AdS${}_3$-Vaidya, a spacetime undergoing gravitational collapse. In the boundary field theory, the collapse corresponds to a quench process where the dual 1+1 dimensional CFT is taken out of equilibrium and subsequently thermalizes. From the two-point function, we extract an effective occupation number in the boundary theory and study how it approaches the thermal Bose-Einstein distribution. We find that the Wightman functions, as well as the effective occupation numbers, thermalize with a rate set by the lowest quasinormal mode of the scalar field in the BTZ black hole background. We give a heuristic argument for the quasinormal decay, which is expected to apply to more general Vaidya spacetimes also in higher dimensions. This suggests a unified picture in which thermalization times of one- and two-point functions are determined by the lowest quasinormal mode. Finally, we study how these results compare to previous calculations of two-point functions based on the geodesic approximation.

15 pages, 12 figures; v2: typos corrected, conclusions clarified; v3: modified section IV, added Appendices A-D, as published in PRD

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• Shear transport far from equilibrium via holography
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• Time Dependent Geometry in Massive Gravity
• Quasinormal modes and thermalization in Improved Holographic QCD
• Notes on frequencies and timescales in nonequilibrium Green's functions
• Quasinormal Modes in Generalized Nariai Spacetimes