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Transient chaos analysis of string scattering

Yoda, Takuya 京都大学 DOI:10.14989/doctor.k24412

2023.03.23

概要

Why chaos?
Almost half a century ago, the black hole information paradox [1, 2] showed inconsistency
between general relativity and quantum mechanics. Although general relativity and quantum
mechanics are great achievements of modern physics, the paradox tells us that there must be
unknown mysteries hidden inside the horizon. It is necessary to identify the appropriate microscopic degrees of freedom and reconcile its microscopic laws with macroscopic phenomena.
Microscopic degrees of freedom of a black hole originate in a highly excited string. The
information paradox motivated the construction of a unitary S-matrix which describes black
hole formation and evaporation [3–6]1 . The idea of the black hole S-matrix was elaborated in
the principle of black hole complementarity2 [10–13]. For a distant observer who phenomenologically describes a black hole as a standard quantum system, its microscopic degrees of
freedom live near the event horizon. Its string interpretation shows that strings tend to form
a single large string, implying that there is a correspondence between black hole states and
highly excited string states [14]. The correspondence has been intensively studied in [14–22]3
to identify the microscopic origin of black holes.
Our next mission will be reconciling the laws of strings with macroscopic phenomena. Its
key lies in black hole chaos. Chaos often refers to the irregularity of microscopic dynamics
which causes thermalization on macroscopic scales. Black holes can be regarded as chaotic
scatterers in the spirit of black hole S-matrix.4 When a particle is shot into a black hole,
its initial condition is apparently forgotten due to thermalization, and it takes a long time
to evaporate due to the redshift near the event horizon (See Fig. 1). These two macroscopic
features imply that there are microscopic irregular dynamics in black holes. The idea of black
hole chaos is supported by the fact that a light ray passing near the event horizon is sensitive
to perturbation of the horizon [7, 8, 24]. In the AdS/CFT correspondence, such sensitivity in
the gravity side corresponds to quantum chaos on the holographic side [25–31].
From the viewpoint of chaos, black holes are distinguished objects. The point of black
hole chaos is that it is associated with an event horizon. Indeed the Lyapunov exponent, a
measure of chaos, is related to surface gravity. ...

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