(i) The entanglement entropy is a UV divergent quantity, while the Bekenstein–Hawking entropy is a finite quantity, defined with respect to Newton’s constant, which has been measured in experiments. How can these two quantities be equal?
(ii) The entanglement entropy is proportional to the number of different field species, which exist in nature. On the other hand, the Bekenstein–Hawking entropy does not seem to depend on any number of fields. This problem is known as the “species puzzle”.
(iii) We have seen that entanglement entropy due to fields, which are non-minimally coupled to gravity, the gauge bosons and gravitons, behave differently from the entropy due to minimally-coupled fields. Since the gauge bosons and gravitons are fields, which are clearly present in nature and thus should contribute to the entropy, does this contribution spoil the possibility of interpreting the black hole entropy as an entanglement entropy?
Living Rev. Relativity 14, (2011), 8
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