Page 22 - Nature Of Space And Time

r=0 singularity

r = 2M
event
horizon

trapped
surface

surface
interior
of star of star

If the Cosmic Censorship Conjecture is correct the trapped surface and the singularity
it predicts can not be visible from far away. Thus there must be a region of spacetime
from which it is not possible to escape to in nity. This region is said to be a black hole.
Its boundary is called the event horizon and it is a null surface formed by the light rays

that just fail to get away to in nity. As we saw in the last lecture, the area of a cross
section of the event horizon can never decrease, at least in the classical theory. This, and
perturbation calculations of spherical collapse, suggest that black holes will settle down to
a stationary state. The no hair theorem, proved by the combined work of Israel, Carter,

Robinson and myself, shows that the only stationary black holes in the absence of matter
elds are the Kerr solutions. These are characterized by two parameters, the mass M and
the angular momentum J. The no hair theorem was extended by Robinson to the case
where there was an electromagnetic eld. This added a third parameter Q, the electric

charge. The no hair theorem has not been proved for the Yang-Mills eld, but the only
di erence seems to be the addition of one or more integers that label a discrete family of
unstable solutions. It can be shown that there are no more continuous degrees of freedom

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