The Quantum Structure of Space and Time (293 pages)

Singularities 53

However, the singularity theorems also apply to classical supergravity theories
in all relevant dimensions since the matter fields satisfy the energy conditions. If
supermatter is added, then only if potentials for scalars are positive (which cannot
happen for pure supergravity) could singularities conceivably be avoided. However
one may also truncate to the pure gravity sector and we are back to the same
problem.
The same problem arises in String Theory in the zero slope limit. Only higher
curvature terms could could conceivably evade the problem.

3.1.2.1 The Strong Energy Condition

I a I

is the most important energy condition (‘Gravity is attractive’).
It can only fail if potentials for scalars are positive.

As an aside , one should note that unless it fails, cosmic acceleration (e.g. a

positive cosmological constant, A > 0, is impossible [27]).
Thus there can be no inflation in pure supergravity theories, or the zero slope
limit of String the~ry.~
If one takes the view that the problem of singularities will be resolved quantum
mechanically, one might be tempted to argue that no particular classical spacetime is
of particular significance, and that classical or semi-classical studies of singularities
are misguided.

At a fundamental level that is probably correct, and is a certainly a valid crit-

icism of much current speculation on the final outcome of Hawking evaporation
for example, but as a practical matter almost all of the large scale universe ap-
pears to be essentially classical. Astrophysicists should not need quantum gravity
to understand X-ray sources or the black hole at the centre of our galaxy.
Thus we need understand better classical singularities.

3.1.3 Cosmic Censorship

The singularities that arise from localised gravitational collapse are associated with

black holes. Intuitively, Penrose’s Cosmic Censorship Hypothesis [all postu-

lates that all singularities are hidden inside the event horizon, i.e. inside I-(T+),

the boundary of the past of future null infinity, I+, the latter is usually assume to

be complete.
Investigating this problem is extremely challenging mathematically. At present

one is limited to looking at spherically symmetric spacetimes coupled to matter,

e.g. massless scalar field, or, in the non-spherical case, to numerical simulations.

4except in models with time-dependent extra dimensions which have other problems