Black Holes by Brian Cox

Author:Brian Cox
Language: eng
Format: epub
Publisher: HarperCollins
Published: 2023-02-03T00:00:00+00:00

Figure 8.2 illustrates the idea. Picture some blob-like region of space and imagine lots of pulses of light flashing from the surface of the blob. For a blob in ordinary flat space, half of the light will head outwards, away from the blob, and the other half will head inwards. That is illustrated on the left of the figure. We’ve only shown five flashes of light, but we imagine many more. The black wavy lines represent light heading out and the grey wavy lines represent light heading inwards. The shaded region is the volume between these two sets of flashes and it will grow with time as the flashes head outwards and inwards at the speed of light. Since nothing travels faster than light, any matter initially sitting on the surface of the blob must stay in the expanding, shaded region. So far so good (hopefully).

On the right we’ve drawn a trapped surface. In this case, both the grey and black flashes are heading inwards. This happens inside the horizon of a black hole due to the curved geometry of spacetime. The converging of the light rays spells trouble. As before, any matter sitting on the trapped surface must stay inside the shaded region because nothing can travel faster than light. But now this region is shrinking down to nothing. In Penrose’s diagram the shaded region labelled F4 corresponds to the shaded region in Figure 8.2.

You might suppose that this is obvious since all matter inside the trapped surface is destined to get squeezed down to nothing, but we should be careful when wielding our dodgy intuition like this. As we’ve learned in the case of the Kerr black hole, matter might slip through a wormhole to explode into an infinite spacetime ‘on the other side’. What Penrose demonstrated rigorously is that at least one in-falling light ray will terminate. The mathematical techniques Penrose employed in his 1965 paper opened the door to a series of successively more wide-ranging singularity theorems, developed mainly by Penrose in collaboration with Stephen Hawking. Significantly, they managed to extend Penrose’s original theorem to include all particles (not just rays of light). They also applied the theorems ‘in reverse’ to show that in general relativity the Universe must have a singularity in the past which, to repeat the quote from the beginning of this book, ‘. . . constitutes, in some sense, a beginning to the universe’.

As something of an aside, it’s notable that the singularity theorems alone do not guarantee that a black hole will form in all circumstances. Black holes are not just singularities; they are black holes because their interior is shielded from their exterior by an event horizon. As we’ve seen, there could conceivably be singularities that are not shielded by a horizon such as the naked singularity in a fast-spinning Kerr black hole. To avoid that possibility, we also need the cosmic censorship conjecture as discussed in Chapter 7.

Naked singularities aside, the only way to avoid the conclusion that black

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