Abstract
We study the entanglement entropy of a one-parameter family of exactly solvable gravities in the 2-dimensional asymptotically-flat space. The islands and Page curves of eternal, evaporating and bath-removed black holes are investigated. The different theories in this parameter class are identified through field redefinitions which leave the island invariant. The Page transition is found to occur at the first a third of the black hole life time in the evaporating case for this family of solutions. In addition, we consider gluing the equilibrium black hole and the evaporating one along a null trajectory and study the effect of gluing on the islands and Page curves. In the glued space, the island jumps across two different geometries at a certain retarded time. As a result, the Page transition is stretched and split into two separate ones -- the first transition happens when the net entropy generation stops and the second one occurs as the early radiation effectively starts to become purified. Finally, we discuss the issues concerning the inconsistent rates of purification and the paradox related to the state of the radiation.
Highlights
AND MOTIVATIONThe issues concerning the purity of Hawking radiation has been around for decades [1,2]
We study the entanglement entropy of a one-parameter family of exactly solvable gravities in the twodimensional asymptotically flat space
A recent breakthrough was made through the gravitational path integral of the replica wormholes geometries, resulting in the formulation of the quantum extremal surface [3,4,5,6,7,8,9,10]
Summary
The issues concerning the purity of Hawking radiation has been around for decades [1,2]. Several models in the asymptotically anti–de Sitter (AdS) space and asymptotically flat space have been explicitly studied, using the approach of quantum extremal surfaces, and are shown to reproduce the corresponding Page curves [9,11,12,13,14,15] This is an indication of the unitarity in the process of Hawking radiation and the consistency with one of the basic principles of quantum mechanics. In the large-N limit, these models incorporate the Hawking radiation, as well as its backreaction on the black hole geometry, and yet still remain exactly solvable This allows us to study the full dynamical process of the. We apply the quantum extremal surface to the study of the dynamical RST-BPP black holes and calculate the entanglement entropy of the black holes in various circumstances. The discussions of our results and issues regarding the rates of purification in the glued and evaporating geometries are presented in the last section
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
