We show using the entropy function formalism developed by Sen (JHEP, 09(2005) 038) that the boundary term which arises from the Einstein‐Hilbert action is sufficient to yield the Bekenstein‐Hawking entropy of a static extremal black hole which is asymptotically flat. However, for asymptotically AdS black holes, the bulk term also plays an important role due to the presence of the cosmological constant. Further, we show that for extremal rotating black holes, both the boundary and the bulk terms contribute non‐vanishing pieces to the entropy.

中文翻译：

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爱因斯坦边界项的熵函数

我们使用 Sen ( JHEP , 09 (2005) 038)开发的熵函数形式证明，由爱因斯坦-希尔伯特作用产生的边界项足以产生渐近平坦的静态极值黑洞的 Bekenstein-Hawking 熵. 然而，对于渐近 AdS 黑洞，由于宇宙常数的存在，体项也起着重要作用。此外，我们表明，对于极值旋转黑洞，边界项和体项都对熵贡献了非消失部分。