Ultraviolet asymptotics and singular dynamics of AdS perturbations - INSPIRE

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Ultraviolet asymptotics and singular dynamics of AdS perturbations

Ben Craps
(
- Intl. Solvay Inst., Brussels and
- Vrije U., Brussels
)
,
Oleg Evnin
(
)
,
Joris Vanhoof
(
- Intl. Solvay Inst., Brussels and
- Vrije U., Brussels
)

Aug 20, 2015

16 pages

Published in:

JHEP 10 (2015) 079

Published: Oct 12, 2015

e-Print:

1508.04943 [gr-qc]

DOI:

10.1007/JHEP10(2015)079

View in:

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Abstract: (Springer)

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

^{2}

. 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.

Note:

15 pages; v4: typos in equation (33) corrected

AdS-CFT Correspondence
Classical Theories of Gravity
Black Holes
Spacetime Singularities
frequency: high
anti-de Sitter
perturbation
higher-dimensional
symmetry: rotation
field theory: scalar

References(18)

Figures(0)

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