Algorithmic characterization of the Kerr-NUT-(A)dS family

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Written by Tim Paetz

One of the most important families of exact solutions to Einstein's vacuum field equations is provided by the Kerr space-time. Usually the Kerr space-time, or, more general, the Kerr-NUT-(A)dS space-time, is given in Boyer-Lindquist-type coordinates, which are adapted to the stationary and axial symmetries of this family. In some situations, though, one may have to deal with coordinate systems which do not reflect these symmetries. In such cases it is convenient to have a gauge-invariant characterization at hand.

Such a characterization has been given by Mars and Senovilla, based on the so-called Mars-Simon tensor. This approach requires the existence of a Killing vector field. To check whether a space-time, given in arbitrary coordinates, belongs to the Kerr-NUT-(A)dS family, one therefore needs to solve the Killing equation first.

In this talk we modify their approach to obtain an algorithmic characterization of the Kerr-NUT-(A)dS family, which avoids the need of solving PDEs. We will do that on a space-time level, and on the level of a Cauchy surface.