Generalised Couch-Torrence Symmetry for Rotating Extremal Black Holes in Maximal Supergravity

Understand

The extremal Reissner-Nordstr\"om black hole admits a conformal inversion symmetry, in which the metric is mapped into itself under an inversion of the radial coordinate combined with a conformal rescaling.

• In the rotating generalisation, Couch and Torrence showed that the Kerr-Newman metric no longer exhibits a conformal inversion symmetry, but the radial equation arising in the separation of the massless Klein-Gordon equation admits a mode-dependent inversion symmetry, where the radius of inversion depends upon the energy and azimuthal angular momentum of the mode.
• It was more recently shown that the static 4-charge extremal black holes of STU supergravity admit a generalisation of the conformal inversion symmetry, in which the conformally-inverted metric is a member of the same 4-charge black hole family but with transformed charges.
• In this paper we study further generalisations of these inversion symmetries, within the general class of extremal STU supergravity black holes.