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Résumé |
The interiors of asymptotically anti-de Sitter (AdS) black holes provide a setting
for extending holographic renormalisation group (RG) flows into a “trans-IR”
regime behind the horizon. In this talk, I will discuss how these flows encode
chaotic dynamics near a spacelike singularity and how that dynamics is reflected
in a holographic probe. I will first show how chaotic Mixmaster dynamics arises in
a class of higher-dimensional AdS black holes. The approach to the singularity
exhibits Belinski–Khalatnikov–Lifshitz (BKL) oscillations, with successive Kasner
epochs separated by transitions described as collisions with effective potential
walls in a Hamiltonian billiard. I will then introduce the thermal a-function as a
holographic diagnostic, interpreted as a measure of effective degrees of freedom
along the flow. This function captures the sequence of Kasner epochs and eras
while decreasing towards zero as the singularity is approached. Finally, I will
discuss the interpretation of this limit as a trans-IR fixed point and conclude
with some possible connections between quasinormal modes, BKL dynamics, and trans-
IR flows.
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