$g_{tt}g_{rr} =-1$ black hole thermodynamics in general quasi-topological gravity

We present a unified framework for the discussion of black hole thermodynamics of $d$-dimensional static black holes with spherical or compact hyperbolic horizon topology satisfying $g_{tt}g_{rr}=-1$ in Schwarzschild gauge. To that end, we consider any such black hole as a solution to an integrable