  Primordial black holes (PBHs) as part of the Dark Matter (DM) would modify
the evolution of large-scale structures and the thermal history of the
universe. Future 21 cm forest observations, sensitive to small scales and the
thermal state of the Inter Galactic Medium (IGM), could probe the existence of
such PBHs. In this article, we show that the shot noise isocurvature mode on
small scales induced by the presence of PBHs can enhance the amount of low mass
halos, or minihalos, and thus, the number of 21 cm absorption lines. However,
if the mass of PBHs is as large as $M_{\rm PBH}\gtrsim 10 \, M_\odot$, with an
abundant enough fraction of PBHs as DM, $f_{\rm PBH}$, the IGM heating due to
accretion onto the PBHs counteracts the enhancement due to the isocurvature
mode, reducing the number of absorption lines instead. The concurrence of both
effects imprints distinctive signatures in the number of absorbers, allowing to
bound the abundance of PBHs. We compute the prospects for constraining PBHs
with future 21 cm forest observations, finding achievable competitive upper
limits on the abundance as low as $f_{\rm PBH} \sim 10^{-3}$ at $M_{\rm PBH}=
100 \, M_\odot$, or even lower at larger masses, in unexplored regions of the
parameter space by current probes. The impact of astrophysical X-ray sources on
the IGM temperature is also studied, which could potentially weaken the bounds.

Cosmology and Nongalactic Astrophysics