Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy

TL;DR

This paper investigates the validity of the holographic principle by analyzing logarithmic and higher order corrections to black hole entropy, revealing conditions under which holography holds or fails at different holographic screens.

Contribution

It demonstrates the conditions for holography to be consistent at the horizon versus spatial infinity, and compares various horizon holography approaches, highlighting discrepancies and universality issues.

Findings

Holography at spatial infinity shows disagreement beyond leading order.

Horizon holography is consistent with an appropriate period parameter.

Different horizon holography models do not fully agree with Carlip's approach.

Abstract

The holographic principle is tested by examining the logarithmic and higher order corrections to the Bekenstein-Hawking entropy of black holes. For the BTZ black hole, I find some disagreement in the principle for a holography screen at spatial infinity beyond the leading order, but a holography with the screen at the horizon does not, with an appropriate choice of a period parameter, which has been undetermined at the leading order, in Carlip's horizon-CFT approach for black hole entropy in any dimension. Its higher dimensional generalization is considered to see a universality of the parameter choice. The horizon holography from Carlip's is compared with several other realizations of a horizon holography, including induced Wess-Zumino-Witten model approaches and quantum geometry approach, but none of the these agrees with Carlip's, after clarifications of some confusions. Some challenging open questions are listed finally.