Page 24 - Nature Of Space And Time

too much because the information would still be inside the black hole even if one couldn't
measure it from the outside. But this is where the second e ect of quantum theory on
black holes comes in. As I will show, quantum theory will cause black holes to radiate
and lose mass. Eventually it seems that they will disappear completely, taking with them
the information inside them. I will give arguments that this information really is lost and

doesn't come back in some form. As I will show, this loss of information would introduce a
new level of uncertainty into physics over and above the usual uncertainty associated with
quantum theory. Unfortunately, unlike Heisenberg's Uncertainty Principle, this extra level
will be rather di cult to con rm experimentally in the case of black holes. But as I will

argue in my third lecture, there's a sense in which we may have already observed it in the
measurements of
uctuations in the microwave background.
The fact that quantum theory causes black holes to radiate was rst discovered by do-
ing quantum eld theory on the background of a black hole formed by collapse. To see how

this comes about it is helpful to use what are normally called Penrose diagrams. However,
I think Penrose himself would agree they really should be called Carter diagrams because
Carter was the rst to use them systematically. In a spherical collapse the spacetime won't
depend on the angles and . All the geometry will take place in the r-t plane. Because

any two dimensional plane is conformal to
at space one can represent the causal structure
by a diagram in which null lines in the r-t plane are at ±45 degrees to the vertical.

I +

surfaces
(t=constant)

+ (r =¥;t =+¥)
centre of
symmetry
r = 0
I 0

two spheres
(r=constant)

_ _
(r =¥;t = ¥)
_
I
Let's start with
at Minkowski space. That has a Carter-Penrose diagram which is a

triangle standing on one corner. The two diagonal sides on the right correspond to the
past and future null in nities I referred to in my rst lecture. These are really at in nity
but all distances are shrunk by a conformal factor as one approaches past or future null

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