Once Before Time - Martin Bojowald [104]
24. Space-time of a naked singularity. While the solid part of the vertical line simply corresponds to a center, as before, an infinitely high matter density is realized in the dash-dotted part. In general relativity, this part can be represented only as an anarchic-singular boundary of space-time. From every one of its points, a light ray can escape to the top right boundary; there is thus no horizon covering the singularity. At the singularity, physical laws break down. No control exists on what happens there. Messages, implications, and instigations of the anarchy can reach outside, rendering all predictions impossible.
The cosmic censorship conjecture is also important from a mathematical perspective. There are, as mentioned, explicitly known exhibitionistic solutions that show their singularity nakedly. But they are of utmost shyness: In all known cases it has been demonstrated that the minutest disturbance, a slight change in the initial state of the collapse, causes an all-covering horizon to form—a truly effective censorship. In general, however, this behavior of cosmic censorship has not been proven yet even though it was formulated four decades ago, in 1969, by Roger Penrose. Ever since, mathematicians and physicists alike have tried to prove it. It has initiated many an important mathematical development, and to this day it remains one of the big challenging problems in general relativity. If one considers that this problem is about principal insights into the predictability of everything happening in space-time, one clearly sees in an impressive way the far-reaching importance of general relativity, and of the current research on its open questions.
25. Penrose diagram for a universe starting with the big bang singularity represented by the dash-dotted line at the bottom edge. Although this singularity is not covered by a horizon either, it is completely different from the naked singularity in figure 24 in that it takes the form of a horizontal rather than vertical line. At the top, the diagram is not drawn completely, since there are different possibilities for the future: As described in chapter 1, depending on the precise form of matter, the universe can either recollapse to a singularity, in which case the diagram would be closed at the top, or expand forever.
ANALOG GRAVITY: BLACK HOLES OF THE ORDINARY
If cosmic censorship is taking place, we can analyze black holes only by their horizons. While a direct investigation with probes is most likely beyond reach, general properties of horizons can possibly be studied in the laboratory. The behavior of space-time itself would not be studied in the analysis, but instead matter in some media that can lead to analogous phenomena is used. The first to notice this was Bill Unruh in 1981, who likes to compare a black hole to a powerful waterfall:4 If the water drops down fast enough, faster than the propagation speed of waves or of sound in water, then an observer—say, a fish communicating by sonar—falling down with the water can no longer transmit signals through the water back to another one staying safely at the upper end. One can often watch this directly as shown in figure 26, for the foaming turbulence down the falls cannot propagate against the stream, upward to where the water remains calm. Rapid waterfalls are only the simplest example for the observation that exotic-seeming phenomena of space-time in general relativity can have analogs in common media such as liquids. Investigating geometric phenomena by means of condensed-matter physics is called analog gravity. (Which, it should perhaps be noted, is not a precursor of “digital gravity,” as might be supposed.)
While a horizon, in this sense, can easily be manufactured, more subtle, challenging problems related to quantum effects are of experimental interest. For black holes, among these issues is Hawking