Entropy functions of BPS black holes in AdS$_4$ and AdS$_6$

TL;DR

The paper introduces entropy-function formalisms for supersymmetric black holes in $AdS_4$ and $AdS_6$, building on prior $AdS_5$/$AdS_7$ results. By extremizing carefully constructed functions of chemical potentials and charges, it reproduces the Bekenstein-Hawking entropies and the charge-chemical potential relations of known BPS black hole solutions, and maps entropy-function variables to black hole quantities. The AdS$_4$ function uses a $U(1)^4$ charge structure with a square-root prepotential, while the AdS$_6$ function encodes a single electric charge with two angular momenta, both yielding consistent real saddles that match BH data. These results illuminate the microscopic links to dual CFT indices (CFT$_3$ and CFT$_5$) and suggest generalizations to broader gauged supergravity settings and prepotential-driven constructions.

Abstract

We find the entropy functions of supersymmetric black holes in AdS$_4$ and AdS$_6$ with electric charges and angular momenta. Extremizing these functions, one obtains the entropies and the chemical potentials of known analytic black hole solutions.