The conservation of information of evaporating black holes is a very natural consequence of unitarity, which is the fundamental symmetry of quantum mechanics. In order to study the conservation of information, we need to understand the nature of the entanglement entropy. The entropy of Hawking radiation is approximately equal to the maximum of entanglement entropy if a black hole is in a state before the Page time, i.e., when the entropy of Hawking radiation is smaller than the entropy of the black hole. However, if there exists a process generating smaller entanglements rather than maximal entanglements, the entropy of Hawking radiation will become smaller than the maximum of the entanglement entropy before the Page time. If this process accumulates, even though the probability is small, the emitted radiation can eventually be distinguished from the exactly thermal state. In this paper, we provide several interpretations of this phenomenon: (1) information of the collapsed matter emitted before the Page time, (2) there exists a firewall or a non-local effect before the Page time, or (3) the statistical entropy is greater than the areal entropy; a monster is formed. Our conclusion will help resolve the information loss paradox by providing groundwork for further research.

We construct the Hayden-Preskill protocol by using a system of spin-1/2 particles and demonstrate the black hole information flows. We first defined an analogous black hole A as a collection of such particles. Second, we take the particles from the black hole to outside to define the analogous system of Hawking radiation B as the outside particles. When the black hole and the radiation have the maximum entanglement at the Page time, we take an entangled pair system C and D. The particles of C fall into the black hole while their counterparts of D remain outside. If we assume the rapid mixing of the particle states in the black hole A ∪ C, can the information of C rapidly escape from the black hole like a mirror? We numerically show that if we turn on the rapid mixing in the black hole, the original information of C rapidly escapes from the black hole to the outside in the form of the mutual information between B and D. On the other hand, if there is not enough mixing between A and C, the information escapes slowly. Hence, we explicitly demonstrate the original conjecture of Hayden and Preskill. We emphasize that enough mixing is an essential condition to make the Hayden-Preskill protocol functionally work. * bjmhk2@dgist.ac.kr

We discuss the possibility that gravitational waves are trapped in space by gravitational interactions in 2-dimensional Jackiw-Teitelboim gravity. In the standard geon (gravitational electromagnetic entity) approach, the active region is introduced to confine gravitational waves spatially.In our approach, however, spacetime dependent traceless metric perturbations, i.e. "gravitational waves" are trapped by the vacuum geometry and can be stable against the backreaction due to the metric fluctuations. We expect that our approach may shed light on finding similar self-trapping solutions in 4-dimensional gravity.

We discuss the possibility that gravitational fluctuations (“gravitational-waves”) are trapped in space by gravitational interactions in two dimensional Jackiw–Teitelboim gravity. In the standard geon (gravitational electromagnetic entity) approach, the effective energy is entirely deposited in a thin layer, the active region, that achieves spatial self-confinement and raises doubts about the geon’s stability. In this paper we relinquish the “active region” approach and obtain self-confinement of “gravitational waves” that are trapped by the vacuum geometry and can be stable against the backreaction due to metric fluctuations.

We consider a simple system consisting of matter, radiation and vacuum components to model the impact of thermal inflation on the evolution of primordial perturbations. The vacuum energy magnifies the modes entering the horizon before its domination, making them potentially observable, and the resulting transfer function reflects the phase changes and energy contents. To