Horizonless ultracompact objects and dark matter in quadratic gravity

TL;DR

This paper demonstrates that quadratic gravity predicts horizonless ultracompact objects more compact than black holes, which could serve as dark matter candidates due to their stability and unique properties.

Contribution

It provides explicit analytic models of horizonless ultracompact objects in quadratic gravity, revealing their potential as dark matter and their avoidance of instabilities.

Findings

UCOs are more compact than Schwarzschild black holes.

These objects are regular and horizonless, avoiding evaporation.

They could constitute a form of dark matter.

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.