Description
Integrable $2D$ dilaton theories play a central role in discussions of black holes in a variety of approaches to classical and quantum gravity. They can be obtained from the spherical reduction of $d\geq 4$ quasi-topological gravities, and in particular onshell configurations for the $2D$ metric and scalar field represent genuine $d$-dimensional vacuum solutions. This talk will discuss the reconstruction of generic $d$-dimensional static spherically symmetric black holes satisfying $g_{tt}g_{rr}=-1$ in Schwarzschild gauge as quasi-topological vacuum solutions, and use this reconstruction to establish a unified framework for their black hole thermodynamics. I will illustrate that the generating function determining $f(r) = -g_{tt}$ in the integrated equation of motion provides the thermodynamic mass in a first law which can be derived for any such black hole by an application of Wald's Noether charge formalism.