2022 Volume 77 Issue 3 Pages 161-166
The behavior of the entropy of the Hawking radiation is investigated by the gravitational path-integral. It is calculated using the replica spacetimes that consist of n-copies of the original spacetime. We found that a wormhole connecting different copies of the spacetime gives an important contribution to the entropy at late stages of the black hole evaporation. It reproduces the so-called Page curve, suggesting that an evaporating black hole obeys the unitary time evolution.