Finiteness of entanglement entropy in a quantum black hole

Abstract

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 in the [1] 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 black hole due to this modification and its relation to Rènyi entropy, higher loop quantum correction and higher spin black holes.

Renyi entropy of the critical O(N) model

“…This conjecture obviously reminds one of the Bekenstein-Hawking entropy formula and the two things indeed seem related in various ways. [11][12][13][14] It needs to be emphasized that the Ryu-Takyanagi conjecture uses only a tiny amount of the full power of Maldacena's duality. In particular in scenarios of AdS 3 /CF T 2 where it has been extensively checked one needs to take the limit of large central charge on the CFT side and by virtue of the Brown-Henneux formula we understand that to be a "semiclassical" limit.…”