# Should all black holes have Bekenstein-Hawking entropy especially in string theory?

There are so many confusing descriptions of how Bekenstein-Hawking entropy binds black holes, and thus the question. I previously asked similar questions, but I realized questions were misleading and confusing, so I am asking a new question.

I do know that Bekenstein-Hawking entropy things really on a correct theory of quantum gravity, and thus is only a conjecture. Thus I am assuming that current string-theoretic approaches/interpretations are valid. Or simply say orthodox approaches.

1. One account states that Bekenstein-Hawking entropy does not work when gravity is really strong - this would be when black holes would shrink so much. Would this be correct, or is Bekenstein-Hawking entropy formula universal, at least for some types of black holes?

2. Should all black holes satisfy Bekenstein-Hawking entropy formula?

3. Is Bekenstein-Hawking entropy referring only to state-independent entropic contribution? This is what I am getting out of Ted Jacobson's Entanglement Equilibrium and the Einstein Equation. Look at page 3, and Ted Jacobson literally matches state-independent contribution to Bekenstein-Hawking entropy, and rest of entropic contribution to be determined by the given state, which in this paper is quantum vacuum. However, by Bekenstein bound, it is said that Bekenstein-Hawking entropy is maximal. So it seems that Bekenstein-Hawking entropy refers to entire entropy, not just state-independent ones. How do I reconcile these together? What would be a correct way of understanding these matters?
• Bekenstein-Hawking entropy refers to all radiation modes - UV and IR, right? BH entropy is a different notion than Hawking radiation. For instance in theories without propagating degrees of freedom there are no Hawking radiation, yet there could be black hole and those would have entropy. – A.V.S. Oct 31 '18 at 14:22
• Edited the question as to reflect the comment above. My mistake. – Mark Ripley-AKS Nov 2 '18 at 5:21

1. The Bekenstein-Hawking entropy $$S=A/4G$$ (in units $$1=k_B=c=\hbar$$) may only become inaccurate if there are corrections from higher-derivative but gravitating terms in Einstein's equations. And that's only the case when the radius of the black hole is really tiny – comparable to the Planck length