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On the chaos bound in rotating black holes

2019/03/31 by Viktor Jahnke, Keun-Young Kim, Junggi Yoon
Physics and Astronomy · #Angular velocity #Black Holes and Theoretical Physics #Black hole (networking) #CHAOS (operating system) #Eikonal equation #Inverse #Lyapunov exponent #Noncommutative and Quantum Gravity Theories #Pulsars and Gravitational Waves Research #Upper and lower bounds #hep-th

paper · pdf · doi:10.1007/jhep05(2019)037

35 pages, 2 figures. v2: references added, typos corrected, and clarifications added to the discussion section

openalex created_date 2019/04/01 · arxiv created 2019/04/12 · openalex publication_date 2019/05/01 · arxiv updated 2019/06/05 · openalex updated_date 2026/08/05

Abstract

A bstract We study out-of-time-order correlators (OTOCs) of rotating BTZ black holes using two different approaches: the elastic eikonal gravity approximation, and the Chern-Simons formulations of 3-dimensional gravity. Within both methods the OTOC is given as a sum of two contributions, corresponding to left and right moving modes. The contributions have different Lyapunov exponents, λL± =(2π )/(β)(1)/(1∓ ℓ Ω) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>λ</mml:mi> <mml:mi>L</mml:mi> <mml:mo>±</mml:mo> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> <mml:mi>β</mml:mi> </mml:mfrac> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>∓</mml:mo> <mml:mi>ℓ</mml:mi> <mml:mi>Ω</mml:mi> </mml:mrow> </mml:mfrac> </mml:math> , where Ω is the angular velocity and ℓ is the AdS radius. Since λL-≤ (2π )/(β)≤ λL+ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>λ</mml:mi> <mml:mi>L</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> <mml:mo>≤</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> <mml:mi>β</mml:mi> </mml:mfrac> <mml:mo>≤</mml:mo> <mml:msubsup> <mml:mi>λ</mml:mi> <mml:mi>L</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math> , there is an apparent contradiction with the chaos bound. We discuss how the result can be made consistent with the chaos bound if one views the parameters β ± = β (1 ∓ ℓ Ω) as the effective inverse temperatures of the left and right moving modes.

Citations