Singularities 61a complete quantum mechanical answer to the problem of singularities but so far
has only been explored at the semi-classical level. Probably all the resources of
StringlM-theory will be required for a full treatment.
3.1.7
The ultimate fate of the singularities inside black holes is inextricably mixed up
with the ultimate end of Hawking Evaporation. It may be shown (e.g. Kodama
[l]) that the well known classical spacetime model incoporating back re-action must
contain a (transient) naked singularity.
However it is by no means clear that the semi-classical approximation applies.One must surely have to take into account the quantum interference of space-
times.
Singularities at the end of Hawking Evaporation
But how to do this?3.1.8 Maldacena’s Conjecture
One way in which this might be achieved is to consider Hawking Evaporation in
Ads. String theory in the bulk is supposedly dual to conformal field theory on the
conformal boundary. The latter is believed to be unitary and non-singular, hence
so must the former.
Much work has been done relating black holes in Ads5 and Af = 4 SU(N)
SUSYM. A more tractable case is Ad&. Using it, Maldacena has suggested [6]
a deep connection between unitarity and the ergodic properties of quantum
fields and this has recently been taken up by Barbon and Rabinovici [14] [15], [16]
and by Hawking himself [7] [8].
However, presumably the case of greatest physical interest Ads4 which has re-
ceived much less attention. Little is known about the CFT.
Klebanov and Polyakov [ 131 have proposed a correspondence valid at weak cou-
pling but this invovles a bulk theory containing infinitely many spins. Apart
from some work of Hartnoll and Kumar [ll] and Warnick[l2], little detailed work
has been done on this case.
Hertog, Horowitz and Maeda have argued [39] [38] that cosmic scensorship is
easier to violate in Ads backgrounds, but the remain uncertainties about the details
[351[371.Bibliography
[l] H. Kodama, Prog. Theor. Phys. 62 (1979) 1434.[2] G. W. Gibbons, G. T. Horowitz and P. K. Townsend, Class. Quant. Grav. 12 (1995)
297 [arXiv:hep-th/9410073].
[3] D. J. Gross and M. J. Perry, Nucl. Phys. B 226, 29 (1983).
[4] R. d. Sorkin, Phys. Rev. Lett. 51, 87 (1983).