The first result suggests that static black holes could exist as limits of increasingly compact static stars, but the second result and conjecture suggest otherwise. This remains an open question. More recent numerical evidence is also not conclusive, and it introduces further possible subtleties to do with the size of the black hole [262, 430].
On very small scales relative to the AdS5 curvature scale, , the gravitational potential becomes 5D, as shown in Equation (40),[262, 430]: Static metrics satisfying the asymptotic AdS5 boundary conditions are found if the horizon is small compared to , but no numerical convergence can be achieved close to . The numerical instability that sets in may mask the fact that even the very small black holes are not strictly static. Or it may be that there is a transition from static to non-static behaviour. Or it may be that static black holes do exist on all scales.
The 4D Schwarzschild metric cannot describe the final state of collapse, since it cannot incorporate the 5D behaviour of the gravitational potential in the strong-field regime (the metric is incompatible with massive KK modes). A non-perturbative exterior solution should have nonzero in order to be compatible with massive KK modes in the strong-field regime. In the end-state of collapse, we expect an which goes to zero at large distances, recovering the Schwarzschild weak-field limit, but which grows at short range. Furthermore, may carry a Weyl “fossil record” of the collapse process.
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