Previously on “Does something prevents primordial black holes to evaporate completely: PART 1”, we saw that in 2003, Chen and Adler argued that primordial black hole doesn’t evaporate completely,. Instead, it exists in the form of Planck-mass remnant with a cross-section on the order of 10¯^{70} m² which makes direct detection nearly impossible. Such black hole remnants have been identified as possible cold dark matter candidates.

But now, in a recently published paper in Astronomical Journal, Samuel Kovacik argued that it’s not completely true, instead, the final stage of the evaporation has a recoil effect which would give the microscopic black hole velocity on the order of 10¯^{1} c which is in disagreement with the cold dark matter cosmological model.

Yeah friends, the temperature as a function of mass, grows very rapidly in the vicinity of m0. This means that, when the black hole has the mass mTmax for which it reaches the maximal temperature, the radiation is so energetic that the mass difference ∆m = mTmax – m0 is radiated in a relatively small amount of quanta, Nq ≈ ∆m / Tmax ≤ 10². Each quantum carries momentum on the order of p ≈ ∆m/√Nq and due to the conservation law the black hole receives the opposite momentum. As the radiation is random so are the momentum impulses the black hole receives. As a result, it performs a random walk in the momentum space, and after radiating Nq quanta will carry momentum of magnitude pr ≈ ∆m/√Nq. As a result, its final recoiled velocity will be on the order of:

This is the recoil effect due to thermal Hawking radiation of Planck-size black holes.

For the considered cases of matter density, they have ∆m / m0 = 0.33/0.26/0.22 and Nαq = 88/8.4/3.8; therefore recoil velocity = 0.03/0.09/0.11. In all three cases, this is a considerable fraction of speed of light (recall that they used units in which c = 1).

The recoil effect due to the Hawking radiation modified by the quantum structure of space discussed by us makes the Planck-size black holes improbable dark matter candidates as during the last moments of radiation they would obtain velocities large enough to be incompatible as cold dark matter. Velocities of the Planck-size black holes would also exceed escape velocities from most astronomical objects.— told Samuel Kovacik, lead author of the study

However, their discussion has not been very detailed as they do not have a detailed description of the quantum gravity and the behaviour of the Hawking radiation on this scale. But, at least under current assumptions they think that the recoil effect due to thermal radiation of microscopic black holes should be taken into consideration.

This research was supported by VEGA 1/0703/20 and the MUNI Award for Science and Humanities funded by the Grant Agency of Masaryk University.

**Reference***: Samuel Kováčik et al., “Hawking-Radiation Recoil of Microscopic Black Holes”, Astronomical Journal, pp. 1-5, 2021. https://arxiv.org/abs/2102.06517*

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