Abstract
The analytic continuation of the general signature (1, 3) Lorentzian Kerr-Taub-NUT black holes to signature (2, 2) Kleinian black holes is studied. Their global structure is characterized by a toric Penrose diagram resembling their Lorentzian counterparts. Kleinian black holes are found to be self-dual when their mass and NUT charge are equal for any value of the Kerr rotation parameter a. Remarkably, it is shown that the rotation a can be eliminated by a large diffeomorphism; this result also holds in Euclidean signature. The continuation from Lorentzian to Kleinian signature is naturally induced by the analytic continuation of the S-matrix. Indeed, we show that the geometry of linearized black holes, including Kerr-Taub-NUT, is captured by (2, 2) three-point scattering amplitudes of a graviton and a massive spinning particle. This stands in sharp contrast to their Lorentzian counterparts for which the latter vanishes kinematically and enables a direct link to the S-matrix.
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Crawley, E., Guevara, A., Miller, N. et al. Black holes in Klein space. J. High Energ. Phys. 2022, 135 (2022). https://doi.org/10.1007/JHEP10(2022)135
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DOI: https://doi.org/10.1007/JHEP10(2022)135