Quote · Dwarkesh Podcast
Adam Brown – A deep but accessible introduction to general relativity
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Black holes are the ultimate power plants
At 49:38 · chapter starts 47:12
Brown walks through three exact formulas from the Schwarzschild solution. First, the gravitational field required to stay static: it goes as GM/r² times a correction factor (1 - 2GM/c²r)^-½, diverging at the Schwarzschild radius. Inside that radius, no rocket can keep you static. Second, gravitational time dilation: your wristwatch deep in the well ticks at a rate reduced by the same square-root factor, confirmed in the 1950s by the Harvard physics department using atomic clocks at different heights [1] — Adam Brown "GPS clocks require GR correction: GPS satellites must account for gravitational time dilation — clocks on Earth's surface run slow relative…" 58:50 and now corrected for in GPS systems. Third, gravitational redshift: photons climbing out of a gravitational well lose energy and shift to lower frequency. Brown notes all three are the same formula in different clothing, and that both gravitational time dilation and special-relativistic time dilation stack when an observer is both deep in a well and moving.
GPS satellites must account for gravitational time dilation — clocks on Earth's surface run slow relative to those in orbit — or navigation would drift and become unusable.
Chemical rockets get 10^-10 of rest-mass energy. Fission gets 0.1%. Fusion gets 1%. A black hole pulley system gets 100% — every last joule. As you lower a brick to just above the event horizon and release it, you've extracted the full mc² before it falls in. Nothing in physics can beat that.
Nuclear fission extracts roughly 10^-3 (0.1%) of rest-mass energy — orders of magnitude better than chemistry but far below the theoretical 100% of a black hole power plant.
Nuclear fusion is more efficient than fission, extracting roughly 1% of rest-mass energy, but still cannot touch the 99% stored in the rest mass of protons and neutrons.
By slowly lowering mass to just above a black hole's event horizon and releasing it, you can in principle extract 100% of the rest-mass energy — the maximum possible by any physical process.
From outside, you never see someone cross the event horizon — they slow, redshift, and fade. From inside, the infaller notices nothing unusual at the horizon. For a galactic-mass black hole, you could cross the event horizon, live your entire life inside, have descendants, and only die when you reach the singularity. Two observers, one event, radically different stories.
