The discovery that black hole entropy was equal to its area divided by 4G inspired the holographic principle which was realized in the AdS/CFT correspondence. The causal holographic information (CHI) proposal conjectures a relationship between coarse-grained entropy in the CFT and the area/4G of a certain surface (CHI surface) in the bulk gravitational theory. Previous research by Zicao Fu and Don Marolf provided evidence that the CHI satisfies a nontrivial bound, the quantum null energy condition (QNEC), which is a generalization of the classical null energy condition of general relativity. In particular, they showed that the QNEC is satisfied on 1+1 dimensional conformal field theory when evaluated on states dual to conical defects in AdS3. This surprising finding supports the idea that the causal holographic information defines a useful notion of coarse-grained holographic entropy. That the QNEC is satisfied for states in a 1+1 dimensional field theory warrants investigation of its general validity. Here we consider the QNEC evaluated on states dual to planar and spherical black holes in AdS4, to determine whether the QNEC remains valid in higher dimensional field theories.
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