Criticality of ISCOs and AdS/CFT

TL;DR

This paper analyzes particle trajectories around black holes in various dimensions, revealing universal features and phase transition-like behavior at the innermost stable circular orbits (ISCOs), with implications for AdS/CFT correspondence.

Contribution

It uncovers topological and universal properties of ISCOs in black hole spacetimes and links these to phase transitions and operator dimensions in dual CFTs.

Findings

Universal features of particle trajectories near black holes.

Existence of a critical point where center and saddle points coalesce.

Negative and positive anomalous dimensions in the dual CFT at ISCO.

Abstract

We study the trajectories of massive particles in spherically symmetric black holes in arbitrary dimensions, and find certain universal features based on the topological classification of the fixed points. If the system admits a center, we find two possible outcomes: regardless of the value of the angular momentum, the center always survives, which is realized in global AdS spacetimes or, the center disappears below a critical value of angular momentum, which happens for various spherically symmetric black holes. For the latter case, we find that irrespective of the details of the black hole, there must always be a saddle point. Topological arguments show that there exists a certain critical value of energy, angular momentum and the angular velocity, where the center and the saddle coalesce. This happens at a special point in the parameter space where the trajectories are the limiting innermost stable circular orbits (ISCOs). At the critical point, conserved quantities show universal, van der Waals-like mean-field scaling typical of a second-order phase transition. The anomalous dimensions $\gamma$ of the double-twist operators in the CFT are found, both using AdS/CFT and through the the heavy-heavy-light-light four point correlators, giving negative and positive values for the center and saddle, respectively, including the emergence of certain non-analytic behaviour at the ISCO. For the center, we also find subleading corrections in $\frac{1}{\Delta_H}$ to $\gamma$ in the dual CFT, and dsicuss the implications of our results.