The event horizon of a black hole equals its quantum-mechanical size, the so-called Compton wavelength, if its mass is 22 micrograms, equivalent to 13 quintillion (roughly 10 to the power 19) protons. For such a black hole, quantum mechanics is as important as gravity. Since we do not have a predictive theory that unifies the quantum world with Einstein’s description of gravity as a curved spacetime, we do not know the fate of these tiny black holes.
In 1974, Stephen Hawking showed that mini black holes evaporate quickly by emitting thermal radiation. However, the temperature of Planck-mass black holes is the Planck temperature, conjectured as the highest energy attainable in nature. As a result, it is possible that Planck black holes are stable and cannot decay. In that case, could they be dark matter? This question was first asked in a 1987 paper by J. H. MacGibbon.
The interaction cross-section of Planck-mass black holes is the Planck length squared, of order 3 times 10 to the power of -65 centimeter squared (expressed as 2Gh/c³, where G is Newton’s constant, h is Planck’s constant and c is the speed of light). This minuscule cross-section translates to an extreme level of sterility, making Planck-mass black holes viable candidates for dark matter.
To make dark matter, there needs to be one Planck-mass black hole per 10 to the power of 27 photons of the microwave background. The inverse of this huge number requires a tiny conversion efficiency of radiation to Planck-mass black holes in the early universe. For example, dark matter could be a relic from a population of mini black holes of larger mass that evaporated early on and left behind Planck-mass black holes as their remnants.
To account for the Milky-Way dynamics, dark matter must have a local mass density equivalent to 0.4 proton masses per centimeter cubed. This translates to one Planck-mass black hole passing through our body per year. Such passages pose a negligible health risk because of the tiny cross-section for interaction that these tiny black holes possess. Existing dark matter experiments place weak upper limits on the cross-section of these tiny black holes.
Planck-mass black holes could be the relics of phase transitions or decay of heavy fields in the early Universe. In 1971, Stephen Hawking suggested that primordial black holes could be electrically charged. However, later it was realized by G. W. Gibbons that any such charge would create an enormous electric field, causing the black holes to lose their charge by the inevitable production of electron-positron pairs, an effect calculated in 1951 by Julian Schwinger. Other reasons to consider charged relics were proposed more recently.
Could tiny black holes grow in mass by accreting matter? As I showed in a recent paper, the accretion of ordinary matter onto tiny black holes is heavily suppressed by quantum mechanics because the horizon size of such black holes is much smaller than the quantum-mechanical size of an atomic nucleus. It is difficult to squeeze a plump prisoner into a tiny prison.
We should find it humbling that after 90 years of observing the sky and searching for dark matter in our laboratories, we still do not know the nature of 85% of the matter budget in the Universe. We are made of the remaining 15% that we label “ordinary matter” but there is an entirely unknown sector of the Universe which is invisible to us. The situation is equivalent to watching a play in which the main characters are invisible, ghost-like, and we infer their existence from the behavior of a small number of visible actors. Given this backdrop, our experience of the dark sector is superficial. If the invisible matter gives rise to invisible stars, planets and life forms, then we miss most of the action in the cosmos by probing these actors merely by their gravitational influence on visible matter.
But there is a potential to learn more in the future. In a recent paper, I showed that the LIGO-Virgo-KAGA observatories are sensitive enough to detect the gravitational signal from stealth spacecraft more massive than a hundred-thousand-ton that move near Earth at close to the speed of light. Future gravitational wave observatories, such as the Laser Interferometer Space Antenna (LISA), would extend this sensitivity to lower masses and speeds and allow us to learn more about the dark cosmic sector.
However, if dark matter is made of tiniest black holes, we might never detect them directly.
ABOUT THE AUTHOR
Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021. The paperback edition of his new book, titled “Interstellar”, was published in August 2024.
