Feasibility of primordial black hole Remnants as dark matter in view of Hawking radiation recoil

Abstract

It has recently been suggested that black hole remnants of primordial origin are not a viable dark matter candidate since they would have far too large a velocity due to the recoil of Hawking radiation. We re-examined this interesting claim in more details and found that it does not rule out such a possibility. On the contrary, for models based on non-commutativity of spacetime near the Planck scale, essentially the same argument can be used to estimate the scale at which the non-commutativity effect becomes important. If dark matter “particles” are non-commutative black holes that have passed the maximum temperature, this implies that the non-commutative scale is about 100 times the Planck length. The same analysis applies to other black hole remnants whose temperature reaches a maximum before cooling off, for example, black holes in asymptotically safe gravity.

Hawking radiation of scalar particles and fermions from squashed Kaluza–Klein black holes based on a generalized uncertainty principle

“…Since such a Planck mass remnant would be a ground state mass of the black hole, the squashed Kaluza-Klein black hole remnant would have no hair. This would be a desirable property as a dark matter [23,24,[52][53][54]64]. If the squashed Kaluza-Klein metric would describe the geometry around a primordial black hole and the generalized uncertainty principle considered in this paper would play an important role in the quantum nature of the black hole, the squashed Kaluza-Klein black hole remnants would be a dark matter candidate.…”

“…At the same time, the heat capacity (20) also vanishes, which implies that the black hole may not exchange its energy with the surrounding environment. Then the generalized uncertainty principle prevents the squashed Kaluza-Klein black hole to completely evaporate and results in the thermodynamic stable remnant, similar to the evaporation of the black holes in the noncommutative model and the asymptotically safe gravity [62][63][64]. From the left panels of the figures 2 and 3, we see that the mass of the black hole remnant M rm increases with increasing β 0 for fixed r ∞ /l p , while it decreases with increasing r ∞ /l p for fixed β 0 .…”

“…It has been shown that the Hawking radiation is sparse throughout the whole Hawking evaporation process of the four-dimensional black hole [66]. However, it has also been shown that the sparsity of the Hawking radiation would be modified by some quantum gravity effects in some higherdimensional black hole spacetimes [64,[67][68][69][70][71][72][73][74]. Further, once the wave effect of the radiation is taken into account, the sparsity becomes a crucial feature that extends the black hole lifetime.…”

“…Then the sparsity of the Hawking radiation is enhanced due to the quantum gravity effect. Thus, similar to the evaporation of the black holes in the noncommutative model and the asymptotically safe gravity [62,64], the squashed Kaluza-Klein black hole with the generalized uncertainty principle would take an infinite amount of time to radiate a particle at the final stage of the evaporation, and then turn into the remnant when the black hole mass M approaches the mass M rm . Since the squashed Kaluza-Klein black hole remnant would not radiate and its gravitational interaction would be very weak, it would be difficult to observe the remnants in our Universe directly.…”

Diffuse emission from black hole remnants

“…The possibility that black holes tunnel into long-living remnants at the end of their evaporation [1][2][3][4][5][6] has recently been receiving renewed attention [7][8][9][10][11][12][13][14]. Here we study the emission that we may expect from such remnants.…”