Page 38 - Nature Of Space And Time
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black hole tunneling through
Euclidean space to annihilate
Euclidean space
matter and information
thrown into black hole
which radiates
Lorentzian space
Euclidean space
black hole tunneling through
Euclidean space to pair create
process; the Hamiltonian with pair creation is the same as the Hamiltonian without.I'm
very grateful to Simon Ross and Gary Horovitz for calculating this reduction just in time
for this lecture. It is miracles like this, and I mean the result not that they got it, that
convince me that black hole thermodynamics can't just be a low energy approximation.
I believe that gravitational entropy won't disappear even if we have to go to a more
fundemental theory of quantum gravity.
One can see from this thought experiment that one gets intrinsic gravitational en-
tropy and loss of information when the topology of spacetime is di erent from that of
at
Minkowski space. If the black holes that pair create are large compared to the Planck
size the curvature outside the horizons will be everywhere small compared to the Planck
scale. This means the approximation I have made of ignoring cubic and higher terms in
the perturbations should be good. Thus the conclusion that information can be lost in
black holes should be reliable.
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