Excluding static and spherically symmetric black holes in Einsteinian cubic gravity

By Antonio De Felice (1 )and Shinji Tsujikawa (2)
1. Center for Gravitational Physics and Quantum Information,
Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto, Japan
2. Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan (Dated: May 15, 2023

Einsteinian cubic gravity is a higher-order gravitational theory in which the linearized field equa- tions 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 static and spheri- cally symmetric vacuum solutions against odd-parity perturbations without imposing the condition f = h. 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, in the regime where the effective field theory is valid, one dynamical degree of freedom has a negative sound speed squared −1/2 for the propagation of high angular momentum modes. Thus, any static and spher- ically symmetric vacuum solutions present in Einsteinian cubic gravity, which includes the black hole solution with f = h, are excluded by ghost and Laplacian instabilities.

For the remainder of the article,
See: https://arxiv.org/pdf/2305.07217.pdf

Einsteinian cubic gravity unveils two further surprising features. The charged black holes do not possess an inner horizon, in contrast with the usual Reissner-Nordström spacetime, thus avoiding the need to resort to strong cosmic censorship to uphold determinism. In addition to black holes, there exists a one-parameter family of naked singularity spacetimes sharing the same mass and charge as the former, but not continuously connected with them. These naked singularities exist in the under-extremal regime, being present even in pure (uncharged) Einsteinian cubic gravity.