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
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 , 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 , 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 [94, 303]:
- 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
where is the number of light degrees of freedom. Using , this gives an evaporation
A more detailed analysis  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 [61, 62, 129,
150, 227, 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, 93, 116]).