A Kolmogorov-Zakharov Spectrum in $AdS$ Gravitational Collapse

Abstract

We study black hole formation during the gravitational collapse of a massless scalar field in asymptotically $Ad{S}_D$ spacetimes for $D=4,5$. We conclude that spherically symmetric gravitational collapse in asymptotically $AdS$ spaces is turbulent and characterized by a Kolmogorov-Zakharov spectrum. Namely, we find that after an initial period of weakly nonlinear evolution, there is a regime where the power spectrum of the Ricci scalar evolves as ${\omega }^{-s}$ with the frequency, $\omega$, and $s\approx 1.7\pm 0.1$.

5 pages, 4 figures. v2: Typos, other initial profile considered for universality, error analysis, close to PRL version

References in corpus (2)

• Relativistic chaos is coordinate invariant
• Turbulence and Chaos in Anti-de-Sitter Gravity

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