Interior Geometry of Charged AdS Black Holes with Scalar Hair

arXiv:2008.12786, arXiv:2205.03365

In the presence of a scalar hair perturbation, the Cauchy horizon of a ReissnerNordström black hole disappears and is replaced by the rapid collapse of the Einstein Rosen bridge, which leads to a Kasner singularity. Before reaching the singularity, there are several intermediate regimes include strong Josephson oscillations in the condensate and possible Kasner inversions in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity. In order to probe the above physical processes inside black hole, we discuss three different geometric objects:  the length of dimension one spacelike curves which is related to correlators of heavy scalar operators in the WKB approximation,  the area of dimension two extremal surfaces which is the holographic dual of the entanglement entropy,  the volume of dimension three extremal bulk surfaces which is dual to complexity in CV conjecture. The result is that only geodesic can detect the geometry deep within the wormhole.