Interview, Fireside Chat
Why Space Elevators Can't Mine Black Holes – Adam Brown
- Black holes represent a potential ultimate energy source for a civilization that has exhausted stars, as they can release stored mass-energy via quantum mechanical processes.
- Prior to the 1970s, it was believed matter and energy could not escape black holes; Hawking and Bekenstein established that quantum mechanics allows energy to leak out as Hawking radiation.
- A solar-mass black hole has a temperature of only nanokelvins, causing it to radiate energy at an extremely slow rate.
- Left unassisted, a solar-mass black hole requires approximately $10^{55}$ times the current age of the universe to fully evaporate.
- "Mining" proposals suggest using a mechanical claw outside the event horizon to drag away Hawking radiation, analogous to a high-performance space elevator.
- A space elevator relies on a tension structure held from above, where the rope's tension increases with altitude, requiring material strength sufficient to support its own weight.
- Steel is insufficient for an Earth-based space elevator, as the required thickness would exceed the Earth's diameter by the time it reaches geostationary orbit.
- Carbon nanotubes offer sufficient tensile strength for an Earth-based space elevator, though engineering challenges regarding length and purity remain.
- For black hole mining, the critical metric is the tensile strength-to-mass ratio; carbon nanotubes possess a ratio of roughly $10^{-12}$, which is inadequate.
- The laws of physics impose a fundamental upper bound on tensile strength relative to mass, determined by the speed of light ($c^2$).
- A fundamental string from string theory represents the theoretical maximum strength possible, but it can only support its own weight with zero capacity to lift a payload.
- Consequently, mechanical mining of solar-mass black holes is deemed physically impossible for extracting usable energy at a useful rate.
- Energy extraction efficiency depends on the black hole's mass; smaller black holes have higher temperatures and radiate energy more rapidly.
- Chemical reactions are highly inefficient, extracting only one part in $10^{10}$ of the rest mass energy of fuel.
- Nuclear reactions improve efficiency to roughly one part in $10^3$ to $10^4$ by utilizing strong nuclear forces, but are still limited by the conservation of baryon number (total protons plus neutrons).
- Because nuclear processes preserve baryon number, they cannot access the majority of the mass-energy stored in protons and neutrons.
- Gravitational interaction is the only known fundamental force that does not conserve baryon number, allowing protons and neutrons to be converted entirely into radiation.
- A black hole can act as a 100% efficient power plant by ingesting baryonic matter and emitting high-energy photons, neutrinos, and gravitons.
- To achieve near-perfect efficiency, a civilization must utilize a small black hole, carefully preventing it from growing while capturing all emitted particles, including elusive gravitons.