April 23, 2015 19:46 ”NC mBH as DM arXiv” NONCOMMUTATIVITY INSPIRED BLACK HOLES AS DARK MATTER CANDIDATE SamuelKov´aˇ cik Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava, Mlynsk´a dolina Bratislava, 842 48, Slovakia samuel.kovacik@fmph.uniba.sk We study black holes with a source that is almost point-like (blurred), rather than exactly point-like, which could be caused by the noncommutativity of 3-space. Depending on its mass, such object has either none, one or two event horizons. It possesses new properties, which become important on microscopic scale, in particular the temperature of its Hawking radiation does not increase infinitely as its mass goes to zero, but vanishes instead. Such frozen, extremely dense pieces of matter are good dark matter candidate. In addition, we introduce an object oscillating between frozen black hole and naked (softened) singularity, such objects can serve as constituents of dark matter too. We call it gravimond. Keywords : Noncommutative quantum mechanics; microscopic black holes; dark matter. PACS numbers: 1. Introduction Quantum theory allowed us to merge three of the four (known) forces of nature within one unified theory. However, its relation with the last one - gravity is, to put it mildly, questionable. At least some of the problems with it are caused by infinitely large energies or equivalently, by zero distances. If the space we live in has some shortest possible distance, those problems would vanish. Noncommutative (NC) theories are formulated in spaces whose coordinates do not commute with each other and therefore one cannot localize their points (this is similar to ordinary quantum mechanics where one cannot exactly know the phase space position of a particle). They could be viewed as effective theories to some higher theory which fuses quantum physics with gravity, yet they already possess a natural energy cut-off a . Black holes are important objects in both classical and quantum gravity which also posses a high-energy ill behavior. As discovered by Hawking, they radiate with a temperature inversely proportional to their mass, thus as they become infinitely small, they also turn infinitely hot. a For example in [13] it has been shown that the spectrum of free Hamiltonian in a NC space has not only a lower boundary but also an upper one 1