Renormalization-group perspective on gravitational critical collapse

In this work, we propose extremal black holes (BH) as critical points of a new class of gravitational collapses. The conjecture is made by observing the continuous self -similarity (CSS) and discrete selfsimilarity (DSS) behaviors of perturbations of an extremal black hole spacetime and compare them to similar properties of Choptuik-type critical solutions. By performing analytical perturbation studies on extremal black holes, we explicitly show that the DSS solution found here can be interpreted as renormalization group (RG) limit cycles, and the transition between CSS and DSS regimes occurs as the stable and unstable fixed points collide and move to the complex plane. We argue that the DSS solutions found in spherically symmetric gravitational collapses can be similarly interpreted. We identify various phenomena in nongravitational systems with RG limit cycles, including DSS correlation function, DSS scaling laws in correlation length, and order parameters, which are observed in gravitational critical collapses. We also discuss a version of gravitational Efimov effect.