On Euclidean and Noetherian Entropies in AdS Space

TL;DR

This paper compares Euclidean and Wald entropy calculations for AdS black holes, demonstrating their agreement even with higher derivative corrections, and provides a general framework for understanding their equivalence.

Contribution

It shows the equivalence of Euclidean and Wald entropy approaches in AdS spaces with higher derivative corrections, including the Type IIB R^4 term.

Findings

Explicit agreement between the two entropy methods for various higher derivative corrections.

Analysis of the leading correction to Bekenstein-Hawking entropy in AdS_5 Schwarzschild black holes.

A general framework explaining the equivalence of Euclidean and Wald entropy calculations.

Abstract

We examine the Euclidean action approach, as well as that of Wald, to the entropy of black holes in asymptotically $AdS$ spaces. From the point of view of holography these two approaches are somewhat complementary in spirit and it is not obvious why they should give the same answer in the presence of arbitrary higher derivative gravity corrections. For the case of the $AdS_5$ Schwarzschild black hole, we explicitly study the leading correction to the Bekenstein-Hawking entropy in the presence of a variety of higher derivative corrections studied in the literature, including the Type IIB $R^4$ term. We find a non-trivial agreement between the two approaches in every case. Finally, we give a general way of understanding the equivalence of these two approaches.