Black Holes in Klein Space

TL;DR

This paper explores the properties of black holes in Kleinian signature, revealing their self-duality, the role of diffeomorphisms in eliminating rotation, and connecting their geometry to scattering amplitudes via analytic continuation.

Contribution

It introduces a novel analysis of Kleinian black holes, showing their self-duality, the invariance of rotation under diffeomorphisms, and links their linearized geometry to scattering amplitudes.

Findings

Kleinian black holes are self-dual when mass equals NUT charge.

Rotation parameter can be removed by a large diffeomorphism.

Linearized black hole geometry is described by three-point scattering amplitudes.

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.