Thermalization of Green functions and quasinormal modes. (English) Zbl 1388.83219

Summary: We develop a new method to study the thermalization of time dependent retarded Green function in conformal field theories holographically dual to thin shell AdS Vaidya space times. The method relies on using the information of all time derivatives of the Green function at the shell and then evolving it for later times. The time derivatives of the Green function at the shell is given in terms of a recursion formula. Using this method we obtain analytic results for short time thermalization of the Green function. We show that the late time behaviour of the Green function is determined by the first quasinormal mode. We then implement the method numerically. As applications of this method we study the thermalization of the retarded time dependent Green function corresponding to a minimally coupled scalar in the \(\mathrm{AdS}_{3}\) and \(\mathrm{AdS}_{5}\) thin Vaidya shells. We see that as expected the late time behaviour is determined by the first quasinormal mode. We apply the method to study the late time behaviour of the shear vector mode in \(\mathrm{AdS}_{5}\) Vaidya shell. At small momentum the corresponding time dependent Green function is expected to relax to equilibrium by the shear hydrodynamic mode. Using this we obtain the universal ratio of the shear viscosity to entropy density from a time dependent process.


83C47 Methods of quantum field theory in general relativity and gravitational theory
83C57 Black holes
83E30 String and superstring theories in gravitational theory
Full Text: DOI arXiv


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