Generalized quasi-topological gravities: the whole shebang

Understand

Generalized quasi-topological gravities (GQTGs) are higher-curvature extensions of Einstein gravity in $D$-dimensions.

• Their defining properties include possessing second-order linearized equations of motion around maximally symmetric backgrounds as well as non-hairy generalizations of Schwarzschild's black hole characterized by a single function, $f(r)\equiv - g_{tt}=g_{rr}^{-1}$, which satisfies a second-order differential equation.
• In arXiv:1909.07983 GQTGs were shown to exist at all orders in curvature and for general $D$.
• In this paper we prove that, in fact, $n-1$ inequivalent classes of order-$n$ GQTGs exist for $D\geq 5$.