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arXiv · 2602.19721

Coarse Graining Holographic Black Holes in Higher Curvature Gravity

Qiongyu Qi
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Abstract

We consider the holographic description of the dynamical black hole entropy in $f(R)$ higher curvature gravity which proposed by Hollands-Wald-Zhang. On the bulk side, we show that the coarse-grained entropy (outer entropy) of a generalized marginally trapped surface corresponds precisely to the Wald entropy associated with this surface. To get this result, we first formulate the AdS/CFT correspondence in the Einstein frame and derive the correspondence between the von Neumann entropy in the Einstein frame and the $f(R)$ frame. This facilitates the derivation of the correspondence between the two outer entropies in the two frames. Furthermore, we directly derive a focusing theorem associated with generalized expansion in $f(R)$ gravity. We then formulate how to construct the stationary null hypersurface for the generalized expansion and the junction condition to glue a hypersurface in $f(R)$ gravity. Combining these results, we directly derive the expression for the outer entropy in the $f(R)$ frame and identify its holographic dual.

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Qiongyu Qi. 2026-02-23. Coarse Graining Holographic Black Holes in Higher Curvature Gravity. https://arxiv.org/abs/2602.19721

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