

4.6 AdS/CFT and black holes
on 1-brane RS-type models
Oppenheimer-Snyder collapse is very special; in particular, it is
homogeneous. One could argue that the non-static exterior arises
because of the special nature of this model. However, the
underlying reasons for non-static behaviour are not special to this
model; on the contrary, the role of high-energy corrections and KK
stresses will if anything be enhanced in a general, inhomogeneous
collapse. There is in fact independent heuristic support for this
possibility, arising from the AdS/CFT correspondence.
The basic idea of the correspondence is that the
classical dynamics of the
gravitational field
correspond to the quantum dynamics of a 4D conformal field theory
on the brane. This correspondence holds at linear perturbative
order [87], so that the RS 1-brane
infinite
brane-world (without matter fields on
the brane) is equivalently described by 4D general relativity
coupled to conformal fields,
According to a conjecture [303
], the correspondence
holds also in the case where there is strong gravity on the brane,
so that the classical dynamics of the bulk gravitational field of
the brane black hole are equivalent to the dynamics of a
quantum-corrected 4D black hole (in the dual CFT-plus-gravity
description). In other words [303
, 94]:
- Quantum backreaction due to Hawking radiation
in the 4D picture is described as classical dynamics in the 5D
picture.
- The black hole evaporates as a classical
process in the 5D picture, and there is thus no stationary black
hole solution in RS 1-brane.
A further remarkable consequence of this
conjecture is that Hawking evaporation is dramatically enhanced,
due to the very large number of CFT modes of order
. The energy loss rate due to evaporation is
where
is the number of light degrees of freedom. Using
, this gives an evaporation timescale [303]
A more detailed analysis [95] shows that this expression should be
multiplied by a factor
. Then the existence of
stellar-mass black holes on long time scales places limits on the
curvature scale that are more stringent than the
table-top limit, Equation (6). The existence of
black hole X-ray binaries implies
already an order of magnitude improvement on the table-top limit.
One can also relate the Oppenheimer-Snyder result
to these considerations. In the AdS/CFT picture, the non-vanishing
of the Ricci scalar, Equation (170), arises from the
trace of the Hawking CFT energy-momentum tensor, as in
Equation (172). If we evaluate the
Ricci scalar at the black hole horizon,
, using
, we find
The CFT trace on the other hand is given by
, so that
Thus the Oppenheimer-Snyder result is qualitatively consistent with
the AdS/CFT picture.
Clearly the black hole solution, and the collapse
process that leads to it, have a far richer structure in the
brane-world than in general relativity, and deserve further
attention. In particular, two further topics are of interest:
- Primordial black holes in 1-brane RS-type
cosmology have been investigated in [150, 61, 129, 227, 62, 287]. High-energy effects
in the early universe (see the next Section 5) can significantly modify the
evaporation and accretion processes, leading to a prolonged
survival of these black holes. Such black holes evade the enhanced
Hawking evaporation described above when they are formed, because
they are much smaller than
.
- Black holes will also be produced in particle
collisions at energies
, possibly well below the
Planck scale. In ADD brane-worlds, where
is not
ruled out by current observations if
, this raises
the exciting prospect of observing black hole production signatures
in the next-generation colliders and cosmic ray detectors
(see [51, 116, 93]).

