Trans-IR flows to black hole singularities

We study analytic continuations of holographic renormalization group (RG) flows beyond their infrared (IR) fixed points. Such ``trans-IR'' are a natural framework for describing physics inside black holes. First, we construct monotonic $a$-function which counts degrees freedom along trans-IR flow. Using this function, argue that the ``thin out'' and vanish when flowing to endpoint, represented by Kasner singularity. then recast well-studied quantum information probes in language flows, finding entanglement complexity from volume generally fail fully probe while 2-point correlations action do so complementary manner.