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Without friction on an ambient medium, all objects fall the same way under the influence of gravity. This was demonstrated during the Apollo 15 mission in 1971, when astronaut David Scott dropped a 1.32-kg aluminum-alloy geological hammer and a 0.03-kg falcon feather simultaneously on the Moon. Because the Moon lacks a substantial atmosphere, both items hit the lunar surface at the exact same time, confirming this equivalence principle which was demonstrated far more exquisitely even earlier on Earth.
As gravity pulls our body towards the center of Earth, the ground is pushing back our feet. This reflects the resistance for compression by the electron clouds which make the atoms in the ground. All forms of sport are shaped by these opposing forces.
However, astronauts floating in space without contact with an external surface do not feel gravity as long as their entire body experiences the same gravitational acceleration. They do feel gravity if the gravitational acceleration of their feet is different than that of their head, because such a difference introduces tension which — if strong enough — could tear their body apart. This so-called tidal acceleration is related to the curvature of spacetime, sourced by the average mass density in their neighborhood. An experimentalist in a free-falling elevator can only probe this spacetime curvature. Without curvature, his body falls in exactly the same way as the elevator does, as if gravity did not exist within the elevator.
The most extreme spacetime curvature is experienced near black holes, whose event horizon defines the volume from where even light cannot escape. The horizon-scale curvature of a black hole is sourced by its mass divided by the volume bounded by its event horizon. Since the event horizon radius scales as the black-hole mass, the curvature scales inversely with the square of that mass.
The curvature of black holes with a mass below the mass of the Sun reflects a mass density above 2×10^{16} grams per cubic centimeter, ten times above the mass density of an atomic nucleus. Since there is no astrophysical environment with a density larger than that, the required mass density implies that no astrophysical process can lead to the formation of black holes below the mass of the Sun. However, since the Universe had a much larger mass density close to the Big Bang, an unknown physical process could have led to the formation of black holes in the mass range of asteroids. Such primordial black holes might constitute a fraction of the invisible dark matter in the present-day Universe.
Black holes may offer enormous financial benefits to technological civilizations that are capable of producing them in their backyard. Artificial black holes can be used as clean energy sources that convert the rest mass of trash to radiation with a typical efficiency of ~10%, a hundred times better than nuclear fission (splitting heavy nuclei) and fourteen times better than nuclear fusion (combining light nuclei). An interstellar spacecraft can be propelled to a few percent of the speed of light by shoveling the interstellar medium along its path to fuel its black hole engine.
The main challenge in producing artificial black holes is the required mass density. The recipe for making a black hole out of rocks is as follows:
“Fill a big enough volume with rocks, so that it matches the event horizon of the corresponding black hole.”
What is the total mass of rocks required to satisfy this condition? Since spacetime curvature scales inversely with the square of a black hole mass and a solar mass black hole corresponds to a horizon mass density that is 10^{16} times larger than solid density, one needs to assemble 100 million solar masses of rock within twice the orbital radius of the Earth around the Sun in order to make a black hole.
Supermassive black holes of 100 million solar masses exist at the centers of massive elliptical galaxies that are tens of times more massive than the Milky-Way. The mass of the black hole at the center of the Milky-Way galaxy, Sagittarius A*, is only 4.3 million solar masses. Its formation required compression of matter to a mass density larger than that of rock.
An interesting question remains: do any of the supermassive black holes of 100 million solar masses represent a cosmic engineering project of an advanced technological civilization?
Black holes with a mass of 100 million solar masses hold an important status in the Universe. If a gravitationally-bound object, like a rocky planet or a star, enters a region with a spacetime curvature sourced by a larger mass density, then this object will be torn apart by gravitational tide.
The average density of the Sun, 1.4 grams per cubic centimeter, is coincidentally comparable to rock density. Since the radius of main-sequence stars is roughly proportional to their mass, this implies that low-mass stars exceed rock density by the square of a solar mass divided by their mass and high-mass stars are more dilute than a rocky planet by the same ratio. This means that a rocky planet would be tidally disrupted near common dwarf stars, but would be swallowed whole near stars more massive than the Sun. We used this insight to explain the origin of the anomalous interstellar meteor IM1 in a paper that I co-authored with Morgan MacLeod here.
These considerations also imply that Sun-like stars can be tidally disrupted by the gravitational tide of a black hole less massive than 100 million solar masses. More massive black holes will swallow a Sun-like star whole.
Astronomers observe the bright flares from tidal disruption events of Sun-like stars all the way to the edge of the observable Universe. In 1997, I published here a simple model that describes the properties of these tidal disruption flares in terms of a black-hole star, a concept that gained renewed interest in recent months in the context of the Little Red Dots discovered by the Webb telescope.
Supermassive black holes are fed by stars, planets and gas in their vicinity. Whether extraterrestrial civilizations are involved in their growth remains to be demonstrated.
