Bekenstein-Hawking black hole entropy formula

introduction

black hole entropy
- not proportional to the volume enclosed by the event horizon
- proportional to the area enclosed by the event horizon\(S_{BH}=\frac{A_{H}}{4}\)
nonzero temperature
- Hawking radiation

Then I discuss Verlinde's scheme and the extent to which it gives a clear case of emergence of gravity. Finally, I give a novel derivation of the Bekenstein-Hawking black hole entropy formula based on Verlinde's scheme
De Haro, Sebastian. “Dualities and Emergent Gravity: AdS/CFT and Verlinde’s Scheme.” arXiv:1501.06162 [gr-Qc, Physics:hep-Th, Physics:physics], January 25, 2015. http://arxiv.org/abs/1501.06162.

Youngsub Yoon, Quantum corrections to the Hawking radiation spectrum, http://arxiv.org/abs/1210.8355v6
Hod, Shahar. “Bekenstein’s Generalized Second Law of Thermodynamics: The Role of the Hoop Conjecture.” arXiv:1511.03665 [astro-Ph, Physics:gr-Qc, Physics:hep-Th], November 11, 2015. http://arxiv.org/abs/1511.03665.
Astorino, Marco. “Microscopic Entropy of the Magnetised Extremal Reissner-Nordstrom Black Hole.” arXiv:1507.04347 [hep-Th], July 15, 2015. http://arxiv.org/abs/1507.04347.