Excluding static and spherically symmetric black holes in Einsteinian cubic gravity with unsuppressed higher-order curvature terms

Abstract: Einsteinian cubic gravity is a higher-order gravitational theory in which the linearized field equations of motion match Einstein's equations on a maximally symmetric background. This theory allows the existence of a static and spherically symmetric black hole solution where the temporal and radial metric components are equivalent to each other ($f=h$), with a modified Schwarzschild geometry induced by cubic curvature terms. We study the linear stability of the static and spherically symmetric vacuum solutions against odd-parity perturbations without dealing with Einsteinian cubic gravity as an effective field theory where the cubic curvature terms are always suppressed relative to the Ricci scalar. Unlike General Relativity containing one dynamical perturbation, Einsteinian cubic gravity has three propagating degrees of freedom in the odd-parity sector. We show that at least one of those dynamical perturbations always behaves as a ghost mode. We also find that one dynamical degree of freedom has a negative sound speed squared $-1/2$ for the propagation of high angular momentum modes. Thus, the static and spherically symmetric hairy black hole solutions realized by unsuppressed cubic curvature terms relative to the Ricci scalar are excluded by ghost and Laplacian instabilities.