Does Something Prevents Primordial Black Holes To Evaporate Completely?: PART 1 (Quantum / Cosmology)

Summary:

Hawking radiation would make microscopic black holes evaporate rapidly which excludes them from many astrophysical considerations. However, Chen and Adler in their paper argued that the quantum nature of space would alter this behaviour: the temperature of a Planck-size black hole vanishes and what is left behind is a 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 dark matter candidates.


In 2003, Chen and Adler argued that, when the gravity effect is included, the generalized uncertainty principle (GUP) may prevent black holes from total evaporation in a similar way that the standard uncertainty principle prevents the hydrogen atom from total collapse.

In the standard view of black hole thermodynamics, based on the entropy expression of Bekenstein and the temperature expression of Hawking, a small black hole should emit black body radiation, thereby becoming lighter and hotter, leading to an explosive end when the mass approaches zero. However Hawking’s calculation assumes a classical background metric and ignores the radiation reaction, assumptions which must break down as the black hole becomes very small and light. Thus it does not provide an answer as to whether a small black hole should evaporate entirely, or leave something else behind, which we refer to as a black hole remnant (BHR).

Numerous calculations of black hole radiation properties have been made from different points of view, and some hint at the existence of remnants, but in the absence of a well-defined quantum gravity theory none appears to give a definitive answer.

A cogent argument against the existence of BHRs can be made: since there is no evident symmetry or quantum number preventing it, a black hole should radiate entirely away to photons and other ordinary stable particles and vacuum, just like any unstable quantum system.

Chen and Alder, in their paper, argued that, when the gravity effect is included, the generalized uncertainty principle (GUP) may prevent black holes from total evaporation in a similar way that the standard uncertainty principle prevents the hydrogen atom from total collapse.

Specifically, they derived the GUP to obtain a modified Hawking temperature, which indicated that there should exist non-radiating Planck-size remnants (BHR) with a cross-section on the order of 10¯70 m² which makes direct detection nearly impossible.

The temperature of such Planck-size black hole vanishes and what is left behind is a Planck-mass remnant with a cross-section on the order. In the ordinary space, small black holes evaporate rapidly. In quantum space, they can be eternal and are very difficult to detect due to their miniscule cross-section. If they contributed significantly to the overall dark matter density, proving it would be difficult as direct detection seems to be impossible.

— told Chen, Lead author of the study.

BHRs are an attractive candidate for cold dark matter since they are a form of weakly massive interacting particles. They also investigated an alternative cosmology in which primordial BHRs are the primary source of dark matter. Their study indicated that their scenario is not inconsistent with basic cosmological facts, but more scrutiny is required before it can become a viable option.

To be continued in next part..


Reference: Pisin Chen, Ronald J. Adler, “Black hole remnants and dark matter”, Nuclear Physics B – Proceedings Supplements, Volume 124, 2003, Pages 103-106, ISSN 0920-5632, https://doi.org/10.1016/S0920-5632(03)02088-7.
https://www.sciencedirect.com/science/article/pii/S0920563203020887


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