1209.4530 (Martin Reiris)

On extreme Kerr-throats and zero temperature black-hole horizons    [PDF]

Martin Reiris

We show that there are no vacuum black holes horizons S over asymptotically flat maximal axisymmetric data sets saturating the universal inequality A(S) >= 8 pi |J(S)|, where A(S) and J(S) are the area and angular momentum of S respectively. As equality is known to be reached (on globally different data sets) when and only when the intrinsic and extrinsic geometry of S is that of an extreme Kerr-throat sphere which has zero surface gravity or "temperature", our statement could be rephrased following this heuristic, as the non-existence of black holes of zero temperature (and topological origin) over asymptotically flat maximal slices in a vacuum space-time. We also show the rigidity of the extreme Kerr-throat data, which allows us to investigate the phenomenon of formation of extreme Kerr-throats along sequences of data sets. We prove our results for data sets in the smooth category, a hypothesis that is not entirely a technicality.

View original: http://arxiv.org/abs/1209.4530