Black Hole Information Paradox and Wormholes

In this talk, I will explain about the recent progress in the black hole information paradox that I am involved with. The information paradox arises when a black hole evaporates by emitting Hawking radiation due to the quantum effects. Time dependence of the entropy of Hawking radiation is diagnosis of information loss caused by the black hole evaporation. If information is not lost, the entropy of Hawking radiation should obey the so-called Page curve. In recent research developments, it was found that “the quantum extremal islands” reproduce the unitary Page curve in an evaporating black hole. I will argue about how the quantum extremal islands are derived from the computation of the entropy of Hawking radiation using the gravitational path-integral.