Finiteness of entanglement entropy in a quantum black hole

A logarithmic but divergent term usually appears in the computation of entanglement entropy circumferencing a black hole, while the leading quantum correction to the Bekenstein-Hawking entropy also takes the logarithmic form. A quench model of CFT within finite Euclidean time was proposed by Kuwakino and Wen ( JHEP , 05 (2015) 099) to regard this logarithmic term as entanglement between radiation and the black hole, and this proposal was justified by the alternative sign for n -partite quantum information. However, this preliminary form suffers from the notorious divergence at its low-temperature limit. In this letter, we propose a modified form for black-hole entanglement entropy such that the divergence sickness can be cured. We discuss the final stage of a black hole due to this modification and its relation to the Renyi entropy, higher-loop quantum correction and higher-spin black holes.