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We discuss the non-linear corrections entering in the calculation of theprimordial black hole abundance from the non-linear radiation transfer functionand the determination of the true physical horizon crossing. We show that thecurrent standard techniques to calculate the abundance of primordial blackholes suffer from uncertainties and argue that the primordial black holeabundance may be much smaller than what routinely considered. This would imply,among other consequences, that the interpretation of the recent pulsar timingarrays data from scalar-induced gravitational waves may not be ruled outbecause of an overproduction of primordial black holes.

How well do we know the primordial black hole abundance? The crucial role of nonlinearities when approaching the horizon