The basic idea of the correspondence is that the classical dynamics of the AdS5 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 AdS5 brane-world (without matter fields on the brane) is equivalently described by 4D general relativity coupled to conformal fields,, 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 [406, 139]:
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  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 AdS5 curvature scale that are more stringent than the table-top limit, Equation (6). The existence of black hole X-ray binaries implies
One can also relate the Oppenheimer–Snyder result to these considerations. In the AdS/CFT picture, the non-vanishing of the Ricci scalar, Equation (176), arises from the trace of the Hawking CFT energy-momentum tensor, as in Equation (178). If we evaluate the Ricci scalar at the black hole horizon, , using , we find
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:
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