# 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} }

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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