Towards the Black Hole Interior

Abstract

This thesis elucidates various aspects of the black hole interior in low-dimensional models of quantum gravity. In Chapter 2, we construct 3 symmetry generators that form a Lie algebra SL(2,R). These generators act on objects in the interior of black hole and either boost or translate them in spacetime, allowing us to explore the interior region. In the dual quantum mechanical description of the black hole, these generators are related to the notion of “operator size” in quantum mechanics, giving a symmetries-based perspective on quantum chaos and teleportation. Chapters 3 and 4 are devoted to exploring novel consequences of non-perturbative quantum effects associated with the black hole interior. In Chapter 3, we show how global symmetries are violated in the black hole interior. Using certain relative entropies defined on the Hawking radiation to diagnose the symmetry violation, one sees a large O(1) violation after the Page time, whereas more conventional scattering amplitudes/correlation functions only receive exponentially suppressed violations. In Chapter 4, we quantify the extent to which the black hole interior is highly sensitive to the specific values of the couplings of the theory. We consider a setup where a black hole is in an entangled superposition of states with an auxiliary reference system. The reference records the specific values of the couplings associated to each of the black hole states. At late times, the entanglement wedge of the reference contains an island, signaling the failure of bulk reconstruction in the black hole interior without precise information about the couplings. This thesis is based on three papers: [1] with Juan Maldacena and Ying Zhao, [2] with Yiming Chen, and [3] with Ahmed Almheiri.