Distorted black holes in Physical Review Letters

Can a black hole have a cube-like horizon (with round edges) or any of the other shapes above? The article "Static Einstein-Maxwell black holes with no spatial isometries in AdS space", by Gr@v member C. Herdeiro and E. Radu, published in Physical Review Letters, shows that it can.


Anti-de-Sitter (AdS) space gives yet another example of how special "standard" black holes are. 

In 1967, Werner Israel established a remarkable and influential result in black hole physics: a static isolated black hole must be spherically symmetric, in Einstein's theory of gravity [Ref.]. This result established the first conerstone for the celebrated black hole uniqueness theorems [Ref.], showing the extraordinary simplicity of isolated black holes in equilibrium, in General Relativity.

Israel also generalized his theorem for the presence of electromagnetic fields, i.e. for the case where instead of the black hole being completely isolated (no matter or any type of non-gravitational field around it), electromagnetic fields can be present. It was still possible to establish that a similar result holds in this case [Ref.].

In the article "Static Einstein-Maxwell black holes with no spatial isometries in AdS space", the authors show that the simple addition of a negative cosmological constant dramatically alters Israel's conclusions. A non-rotating equilibrium BH can be distorted away from spherical symmetry to the point of not being invariant under any type of rotation. That is, physically acceptable black hole solutions, exhibiting no pathologies on and outside the horizon, can have an event horizon which has the geometry of say, a cube with smooth edges, as in the middle panel of the figure above.

A negative cosmological constant makes gravity more attractive and spacetime becomes effectively a confining “box”, called Anti-de-Sitter spacetime. This confinement allows electromagnetic fields to form smooth static lumps of pure electromagnetic energy - a fact only observed recently by the same authors [Ref.] -, and these lumps can take peculiar shapes. A BH can then be placed at the centre of such a lump of energy, and its horizon adapts to the shape of the latter, distorting its, otherwise, spherical shape. For instance, the distorted black hole horizons displayed above occur when placing the black hole horizon "inside" the lumps of electromagnetic energy shown below. As it can be observed, the horizon adapts to the shape of the soliton (but without "holes"!).

This is the first time, in the 100 years history of black hole solutions, that an equilibrium black hole without any spatial symmetry (without pathologies and with reasonable asymptotics), is explicitly constructed as a fully non-linear solution of Einstein's field equations.


Gr@v papers in Physical Review Letters

The article "Static Einstein-Maxwell black holes with no spatial isometries in AdS spaceis the third paper published by Gr@v members in the very prestigious Physical Review Letters in 2016. The two previous papers were "Warm Little Inflaton", co-authored by J. G. Rosa, which was chosen as "Editor's suggestion", and  "Explosion and final state of an unstable Reissner-Nordstrom black hole" co-author by C. Herdeiro.

The list of papers published in Physical Review Letters by group members in the last five years also includes "Shadows of Kerr black holes with scalar hair", by P. Cunha, C. Herdeiro, E. Radu and H. Rúnarsson, which was chosen to feature on the cover of the issue wherein it was published, "Kerr black holes with scalar hair", by C. Herdeiro and E. Radu, which became the most cited paper amongst all non-review papers posted in the [gr-qc] arXiv in 2014, and "Radiation from a D-dimensional collision of shock waves: a remarkably simple fit formula", by F. Coelho, C. Herdeiro and M. Sampaio.