Black hole solutions of three dimensional E6-gravity

This paper aims to construct exceptional Bañados–Teitelboim–Zanelli (BTZ) black holes carrying E6 charges as solutions to the 3D higher spin Anti-de Sitter gravity with E6 boundary conditions. Guided by Tits-Satake graphs of real forms of the e6 Lie algebra, we build three remarkable E6-higher spin black hole models: the linear-exceptional and the ortho-exceptional BTZ solutions result from splitting the extremal nodes in the E66 Tits-Satake diagram while the pure exceptional-exceptional model follows from the folding down to F44. And with the help of Hasse diagram visualizations, we study the ensuing higher spin spectrums to develop the corresponding metrics using two types of gauge transformations. For completeness, we examine the thermodynamics of the standard BTZ coupled to E6 higher spin gravity fields by computing the partition function exploiting a one to one correspondence between the factors of the vacuum characters and the roots of the E6 root system.