**Authors:**

(1) Antonio Riotto, Département de Physique Theorique, Universite de Geneve, 24 quai Ansermet, CH-1211 Geneve 4, Switzerland and Gravitational Wave Science Center (GWSC), Universite de Geneve, CH-1211 Geneva, Switzerland;

(2) Joe Silk, Institut d’Astrophysique, UMR 7095 CNRS, Sorbonne Universite, 98bis Bd Arago, 75014 Paris, France, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore MD 21218, USA, and Beecroft Institute of Particle Astrophysics and Cosmology, Department of Physics, University of Oxford, Oxford OX1 3RH, UK.

## Table of Links

2.1 What is the abundance of PBHs?

2.2 What is the effect of PBH clustering?

2.3 What fraction of the currently observed GW events can be ascribed to PBHs?

3.3 Plugging the pair instability gap with PBH?

3.4 PBH eccentricity, 3.5 PBH spin and 3.6 Future gamma-ray telescopes

## 2.4 Are PBHs the Dark Matter?

The idea that PBH can comprise most of the dark matter is one of the main motivations for studying PBH. Unfortunately, observational constraints eliminate this possibility for most of the range of possible PBH masses, with a notable exception around asteroid mass PBH, spanning several decades in mass around ~ 10-12 Mo down to the limit ~ 10-10 Mo, obtained from the isotropic x-ray and soft gamma-ray background observational limits on fluxes produced by PBHs currently undergoing Hawking evaporation [14].

In the standard formation scenario of PBH, it is unavoidable that gravitational waves are generated with a frequency which today is in the mHz range, exactly where the LISA mission has maximum sensitivity [15]. The scenario of PBH as dark matter can be therefore tested in the future by LISA by measuring the GW two-point correlator. The fact that the asteroid mass range is still unconstrained is due to the fact that the microlensing constraints are ineffective around the value 10-11 Mo under which the geometric optics approximation is no longer valid and the constraints from the presence of neutron stars in globular clusters is based on extreme assumptions about the dark matter density. It is of tantamount importance to come out with possible ideas for constraining or identifying PBH in the asteroid mass range.

One promising approach is that PBH capture leads to neutron star conversion to BH. This could occur in dense star clusters that contain DM, as may be the case for nuclear star clusters, and NS conversion would occur in the case of capture of such "endoparasitic" PBHs for PBH masses larger than ~ 10-11 Mo 16]. Such a phenomenon may produce a deficit of pulsars in our GC as possibly observed [17]. Another interesting avenue is to observe the number of massive main-sequence stars in ultra-faint dwarfs which should be suppressed if the dark matter is made of asteroid-mass PBHs |18, making measuring the mass distribution of stars depleted in the high-mass range.

Furthermore, near-extremal PBHs provide an intriguing means of making evaporating PBHs stable on cosmological scales. Formation is simplest for low mass five-dimensional PBHs that initially act like four-dimensional PBHs, Hawking radiating down to the radius of the extra dimension where their effective temperature is effectively zero, to attain a stable mass [19]. These are generated in higher dimensional scenarios and Hawking radiation is generically found to be slowed down [20]. Other scenarios for producing near-extremal PBH include formation of maximally rotating or charged PBH at very early epochs [21], as well as via the quantum gravity phenomenon of so-called memory burden suppression [22]. Detectability is feasible down to scales as small as a few Planck masses for charged PBH relics via terrestrial detectors [23] or equally for high energy particle emission from occasional binary merger events [24].

This paper is available on arxiv under CC BY 4.0 DEED license.