Horizonless ultracompact objects and dark matter in quadratic gravity

Abstract

We show that in quadratic gravity sufficiently light objects must be horizonless and construct explicit analytic examples of horizonless ultracompact objects (UCOs), which are more compact than Schwarzschild black holes. Due to the quadratic terms, gravity becomes soft and eventually vanishes in the high-energy limit leading to a "linearization mechanism": light objects can be described by the linearized theory when their Schwarzschild radius is smaller than the Compton wavelength of the new gravitational degrees of freedom. As a result, we can analytically describe UCOs with a mass-to-radius ratio higher than for a Schwarzschild black hole. The corresponding spacetime is regular everywhere. We show that the Ostrogradsky instabilities can be avoided and discuss the relation with the Higgs vacuum metastability. Due to the lack of a horizon, light UCOs do not evaporate. Therefore, they may play the role of dark matter. We briefly discuss their phenomenology.