Singularities^67with general relativity [Ill.
Despite all these examples, it is simply not true that all singularities are removed
in string theory. Nonlinear gravitational plane waves are not only vacuum solutions
to general relativity, but also exact solutions to string theory [12]. These solutions
contain arbitrary functions describing the amplitude of each polarization of the
wave. If one of the amplitudes diverge at a finite point, then the plane wave is
singular. One can study string propagation in this background and show that
in some cases, the string does not have well behaved propagation through this
curvature singularity [13]. The divergent tidal forces cause the string to become
infinitely excited.
It is a good thing that string theory does not resolve all singularities. Consider
the Schwarzschild solution with M < 0. This describes a negative mass solution
with a naked singularity at the origin. If this singularity was resolved, there would
be states with arbitrarily negative energy. String theory would not have a ground
state. This argument, of course, is not restricted to string theory but applies to any
candidate quantum theory of gravity.
One of the main goals of quantum gravity is to provide a better understand-
ing of the big bang or big crunch singularities of cosmology. Perhaps the most
fundamental question is whether they provide a true beginning or end of time, or
whether there is a bounce. Hertog and I have recently studied this question using
the AdS/CFT correspondence [14], which states that string theory in spacetimes
which are asymptotically anti de Sitter (AdS) is equivalent to a conformal field
theory (CFT). We found supergravity solutions in which asymptotically Ads initial
data evolve to big crunch singularities [15]. The dual description involves a CFT
with a potential unbounded from below. In the large N limit, the expectation value
of some CFT operators diverge in finite time. A minisuperspace approximation
leads to a bounce, but there are arguments that this is not possible in the full CFT.
Although more work is still needed to completely understand the dual description,
this suggests that a big crunch is not a big bounce [15].
Acknowledgment: Preparation of this comment was supported in part by
NSF grant PHY-0244764.Bibliography
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