3.11 Entanglement entropy as one-loop quantum correction

A natural point of view on the entanglement entropy of a black hole is that this entropy, as was suggested by Callan and Wilczek [33Jump To The Next Citation Point], is the first quantum correction to the Bekenstein–Hawking entropy6. Indeed, the Bekenstein–Hawking entropy SBH can be considered as classical, or tree-level, entropy. If we restore the presence of the Planck constant ¯h the Bekenstein–Hawking entropy SBH is proportional to 1∕¯h while the entanglement entropy Sent is an 0 ¯h quantity. The total entropy of a black hole is then the sum
S = SBH + Sent, (111 )
where all particles that exist in nature contribute to the entanglement entropy Sent.
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