Geometries for black hole horizons

Abstract

The application of the blackfold effective theory to the perturbative construction of black holes in higher-dimensions is reviewed. Several solutions with non-trivial horizon geometry and topology are described, such as black helicoidal branes and helicoidal black rings. This hints into a very rich phase diagram for higher-dimensional neutral asymptotically flat black holes.

Instabilities of thin black rings: closing the gap

“…16 On the other hand, the analysis performed here is more accurate for large modes m 1 for which, within this approach and up to second order, no elastic instability is found in any dimension D. This suggests that there is a value of ν that marks the onset for the elastic instability and that due to the requirement (4.7), our analysis is only valid for very thin rings which lie in a region of parameter space below that onset. 17 We observe in the work of [12] that the growth rate of the elastic instability for ν = 0.15 is close to zero, giving some rationale for this interpretation and, in addition, unpublished numerical results [41] substantiate this picture. It may be the case that signatures of the elastic instability appear at third or higher order but to push the blackfold approximation beyond second order is as a daunting task as it is useless since it would require a very high number of derivative corrections, making the effective theory impractical.…”

“…Besides having proved to be extremely useful in finding new black hole solutions [14][15][16][17][18] in asymptotically flat space, we demonstrate here that the blackfold approach [7,19] is a powerful tool for studying hydrodynamic (i.e. Gregory-Laflamme) and elastic instabilities of higher-dimensional black holes in the ultraspinning regime and away from it.…”

“…This work only dealt with boosted black strings and black rings but the method we have provided here, and the complete characterisation of the black brane stress tensor up to second order in derivatives in app. A, is sufficient for studying the dynamical stability of a plethora of different uncharged asymptotically flat black hole solutions, such as helical black rings, Myers-Perry black holes and helicoidal black rings [14][15][16][17]. We plan on returning to this general analysis in the future.…”

“…Additionally, we find a long-lived mode that describes a wiggly time-dependent deformation of a black ring. We comment on disagreements between our results and corresponding ones obtained from a large D analysis of black ring instabilities.Besides having proved to be extremely useful in finding new black hole solutions [14][15][16][17][18] in asymptotically flat space, we demonstrate here that the blackfold approach [7, 19] is a powerful tool for studying hydrodynamic (i.e. Gregory-Laflamme) and elastic instabilities of higher-dimensional black holes in the ultraspinning regime and away from it.…”