Non-Schwarzschild Primordial Black Holes as Dark Matter in Quadratic Gravity

Abstract: One-loop renormalised quantum effective action for gravity contains quadratic in curvature terms. We have found an approximate analytic black hole solution in quadratic gravity by keeping only the radial spherically symmetric fluctuations and dimensionally reducing the 4-dimensional (4D) theory down to the 2-dimensional (2D) dilaton gravity with a potential. The solution reduces to the Schwarzschild black hole in the limit of Einstein's gravity, but otherwise admits non-negative Arnowitt-Deser-Misner (ADM) and positive quasi-local Misner-Sharp masses that can differ significantly. We then study the thermodynamics of such quantum corrected black holes and compute their lifetime under Hawking evaporation. We note that for some range of parameters, black holes increase in mass while emitting Hawking radiation. This pathological behaviour is related to the negative energy states that are present in quadratic gravity. We also find that the micro-lensing of non-Schwarzschild black holes could significantly deviate from the micro-lensing of their Schwarzschild counterparts. These findings have important ramifications for the phenomenology of primordial black holes (PBHs) as dark matter. In particular, the quoted constraints on PBH dark matter from micro-lensing data can be completely evaded, thus making PBHs in the mass range $\sim 10^{-12} - 10~M_{\odot}$ viable dark matter candidates.