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A blackboard was covered with equations, thick as leaves on a walk, and three sentences in English: Price's Theorem: Whatever can be radiated is radiated. Schutz's Observation: Whatever is radiated can be radiated. Things can be radiated if and only if they are radiated.
This quote requires some explanation. "Schutz's observation" was facetious, but Price's theorem, "Whatever can be radiated is radiated," was a serious confirmation of a 1969 speculation by Roger Penrose.Price's theorem is illustrated by the implosion of a mountain-endowed star. Figure 7.4 depicts the implosion. The left half of this figure is a spacetime diagram of the type introduced in Figure 6.7 of Chapter 6; the right side is a sequence of snapshots of the star's and horizon's shape as time passes, with the earliest times at the bottom and the latest at the top.As the star implodes (bottom two snapshots in Figure 7.4), its mountain grows larger, producing a growing, mountain-shaped distortion in the star's spacetime curvature. Then, as the star sinks inside its critical circumference and creates a black hole horizon around itself (middle snapshot), the distorted spacetime curvature deforms the horizon, giving it a mountain-like protrusion. The horizon's protrusion, however, cannot live long. The stellar mountain that generated it is now inside the hole, so the horizon can no longer feel the mountain's influence. The horizon is no longer being forced, by the mountain, to keep its protrusion. The horizon ejects the protrusion in the only way it can: It converts the protrusion into ripples of spacetime curvature (gravitational waves-Chapter 10) that propagate away in all directions (top two snapshots). Some of the of the ripples go down the hole, other fly out into the surrounding Universe, and as they fly away, the ripples leave the hole with a perfectly spherical shape.
How does this mountain-endowed implosion relate to Price's theorem? According to the laws of physics, the horizon's mountain-like protrusion can be converted into gravitational radiation (ripples of curvature). Price's theorem tells us, then, that the protrusion must be converted into gravitational waves, and that this radiation must carry the protrusion completely away. This is the mechanism that makes the hole hairless.