An exact five dimensional Weyl-Geometry Gauss-Bonnet Black Hole

We present a new exact black hole solution of a 5-dimensional Weyl-geometry Gauss-Bonnet theory of gravity. The Euclidean sector defines a fully regular metric coupled to the Weyl vector field. The Euclidean action and entropy are computed, with the latter following the simple $A\mathrm{/}4$ form plus a term linear in the horizon radius, characteristic of Gauss-Bonnet couplings.