Chaotic Motion near Black Hole and Cosmological Horizons

Abstract

It is known that certain types of particle motion near black hole horizons are chaotic while it has been proposed the existence of a universal bound for their Lyapunov exponent. We discuss the relation between chaos and inaffinity in presence of black hole and cosmological horizons. We argue that although a relation between the Lyapunov exponent and the generalized surface gravity appears naturally, in general there is no reason for the Lyapunov exponent of classical trajectories to be bounded in generic spacetimes with horizon. Moreover, we show that the de Sitter spacetime and cosmological horizons act as a nest of chaos in holography and we find that the Lyapunov exponent of the trajectories is related to the inaffinity in the same way for both cosmological and black hole horizons. This suggests that there is no distinction by the Lyapunov exponent between maximal chaos of black hole and cosmological horizons.

Correlation functions for open strings and chaos

“…By itself this is not surprising: a local instability can lead to a growing mode even in a trivially integrable system, the simplest example being the inverse chaotic oscillator [57]. This is similar to findings of [31] where it is noted that horizons are really sources of instability in the bulk. Even integrable systems can display local instability in the vicinity of thermal horizons.…”

“…In our first example we closely follow the idea of [31] and study bulk motion in a broad class of bulk geometries: hyperscaling-violating horizons at finite temperature, constructed in [58][59][60][61] as gravity duals of effective field-theories with scaling and long-range entanglement, thought to be ubiquitous in quantum-many body systems. In [31], it is shown that the bulk geodesics, i.e.…”

“…Among the many questions which have opened up, there is one seemingly technical but in fact physically important subtlety. Several papers have reported the saturation of the bound 2πT for bulk orbits of particles [22,23], or its slight modification/generalization for fields [22] and strings [24][25][26][27][28][29][30]; the systematic answer to the question of the bulk Lyapunov exponent is given in [31]. However, a very simple question arises: why should there ever be JHEP04(2024)025 an MSS-like bound for bulk Lyapunov exponents?…”

Bound on the Lyapunov exponent in Kerr-Newman black holes via a charged particle

“…It is known that the geodesic in a black hole can be chaotic, and this black hole chaos has been researched in [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. According to Hashimoto and Tanahashi [26], it is assumed that the Lyapunov exponent of a particle in a black hole has an upper bound near the horizon.…”

Report on Chaos Bound Outside Taub-Nut Black Holes

“…This sensitivity is represented by a Lyapunov exponent. A lot of work has been done on the chaos and exponent [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Focusing on the near-horizon region of the black hole, Hashimoto and Tanahashi studied the chaos generated by the radial motion of the particle [30].…”