Ultraviolet asymptotics and singular dynamics of AdS perturbationsReport as inadecuate

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Journal of High Energy Physics

, 2015:79

First Online: 12 October 2015Received: 04 September 2015Accepted: 16 September 2015 Abstract

Important insights into the dynamics of spherically symmetric AdS-scalar field perturbations can be obtained by considering a simplified time-averaged theory accurately describing perturbations of amplitude ε on time-scales of order 1-ε. The coefficients of the time-averaged equations are complicated expressions in terms of the AdS scalar field mode functions, which are in turn related to the Jacobi polynomials. We analyze the behavior of these coefficients for high frequency modes. The resulting asymptotics can be useful for understanding the properties of the finite-time singularity in solutions of the time-averaged theory recently reported in the literature. We highlight, in particular, the gauge dependence of this asymptotics, with respect to the two most commonly used gauges. The harsher growth of the coefficients at large frequencies in higher-dimensional AdS suggests strengthening of turbulent instabilities in higher dimensions. In the course of our derivations, we arrive at recursive relations for the coefficients of the time-averaged theory that are likely to be useful for evaluating them more efficiently in numerical simulations.

KeywordsAdS-CFT Correspondence Classical Theories of Gravity Black Holes Spacetime Singularities ArXiv ePrint: 1508.04943

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Author: Ben Craps - Oleg Evnin - Joris Vanhoof

Source: https://link.springer.com/


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