Abstract
We study quantum chaos of rotating BTZ black holes in Topologically Massive gravity (TMG). We discuss the relationship between chaos parameters including Lyapunov exponents and butterfly velocities from shock wave calculations of out-of-time-order correlators (OTOC) and from pole-skipping analysis. We find a partial match between pole-skipping and the OTOC results in the high temperature regime. We also find that the velocity bound puts a chaos constraint on the gravitational Chern-Simons coupling.
Highlights
Is a small parameter that typically depends on the parameters of the theory such as the characteristic energy scale of the operators V and W, and the number of degrees of freedom
We study quantum chaos of rotating BTZ black holes in Topologically Massive gravity (TMG)
We discussed the relations between the quantum chaos parameters including Lyapunov exponents and butterfly velocities from of-time-order correlators (OTOC) and from pole skipping in systems dual to rotating BTZ black holes in Topologically Massive Gravity (TMG), which turns out to be a non-maximally chaotic system at high temperautre
Summary
The focus of our work is quantum chaos for rotating BTZ black holes in three dimensional theories of gravity and we begin with a short review of basic facts about the rotating BTZ black holes. The three dimensional BTZ black holes are vacuum solutions of both Einstein. In most parts of this paper related to pole-skipping, we will assume that the coordinate φ is noncompact This assumption has been widely used in the holographic studies of rotating BTZ, e.g. The parameters r+ and r− are related to the ADM mass M , angular momentum J, Hawking temperature T , and angular potential Ω of the black hole through. A rotating BTZ black hole metric can always be brought to a non-rotating form by a coordinate transformations as shown in the appendix A.1. The ingoing Eddington-Finkelstein coordinates and Kruskal coordinates of BTZ are shown in A.2 and A.3 respectively These coordinates are useful for different purposes and after the calculations we will transform back to metric (2.1) to interpret the physics of quantum chaos
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