# Black Hole Entropy and Finite Geometry

@article{Levay2009BlackHE,
title={Black Hole Entropy and Finite Geometry},
author={P'eter L'evay and Metod Saniga and P{\'e}ter Vrana and Petr Pracna},
journal={Physical Review D},
year={2009},
volume={79},
pages={084036}
}
• Published 3 March 2009
• Mathematics
• Physical Review D
It is shown that the ${E}_{6(6)}$ symmetric entropy formula describing black holes and black strings in $D=5$ is intimately tied to the geometry of the generalized quadrangle GQ(2, 4) with automorphism group the Weyl group $W({E}_{6})$. The 27 charges correspond to the points and the 45 terms in the entropy formula to the lines of GQ(2, 4). Different truncations with 15, 11 and 9 charges are represented by three distinguished subconfigurations of GQ(2, 4), well known to finite geometers; these…
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