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 [33
], is the first quantum correction to the Bekenstein–Hawking
entropy.
Indeed, the Bekenstein–Hawking entropy
can be considered as classical, or tree-level, entropy. If we
restore the presence of the Planck constant
the Bekenstein–Hawking entropy
is proportional to
while the entanglement entropy
is an
quantity. The total entropy of a black hole is then
the sum
where all particles that exist in nature contribute to the entanglement entropy
.