Joerg Hennig (Otago): Investigation of stationary n-black-hole configurations with soliton methods

An intriguing open problem in general relativity is the question as to whether stationary equilibrium configurations with clearly separated bodies can exist. Due to the nonlinear effect of the spin-spin repulsion of rotating objects, and perhaps by considering charged objects with an additional electromagnetic repulsion, it remains a possibility that such unusual configurations do exist. An important example of an n-body system is a (hypothetical) equilibrium configuration with n aligned rotating and possibly charged black holes. By studying the linear matrix problem that is equivalent to the Einstein (-Maxwell) equations for axixymmetric and stationary (electro) vacuum spacetimes, we obtain the most general form of the boundary data on the symmetry axis in terms of a finite number of parameters. This will be illustrated with the simplest case of one black hole in vacuum, and we briefly discuss how an electromagnetic field can be included and the discussion be extended to arbitrary n. In the simplest case n=1, this leads to a constructive uniqueness proof of the Kerr (-Newman) solution. For n=2 and vacuum, one obtains non-existence of stationary two-black-hole configurations. For n=2 with electrovacuum, and for larger n, it remains an open problem whether the well-defined finite solution families contain any physically reasonable solutions, i.e. spacetimes without naked singularities, magnetic monopoles and struts.