Through replica wormholes to the solution of the information paradox

I will discuss the formulation of the information paradox in black hole physics in terms of the time dependence of the entanglement entropy of Hawking radiation. As an introduction, I will discuss the replica trick for calculating the entanglement entropy using a path integral on Riemann surfaces in conventional quantum field theories without gravity. Then, following arXiv:1911.12333, I will reproduce the logic and basic calculations of the entanglement entropy of Hawking radiation in the two-dimensional JT gravity using the replica trick. This calculation is of interest because it allows us to obtain the so-called "island formula" for the entanglement entropy, which leads to a time dependence consistent with the unitary evolution of a black hole.