Positive Energy Functional for Massless Scalars in Rotating Black Hole Backgrounds of Maximal Ungauged Supergravity

Understand

We outline a proof of the stability of a massless neutral scalar field $\psi$ in the background of a wide class of four dimensional asymptotically flat rotating and ``electrically charged'' solutions of supergravity, and the low energy limit of string theory, known as STU metrics.

• Despite their complexity, we find it possible to circumvent the difficulties presented by the existence of ergo-regions and the related phenomenon of super-radiance in the original metrics by following a strategy due to Whiting, and passing to an auxiliary metric admitting an everywhere lightlike Killing field and constructing a scalar field $\Psi$ (related to a possible unstable mode $\psi$ by a non-local transformation) which satisfies the massless wave equation with respect to the auxiliary metric.
• By contrast with the case for $\psi$, the associated energy density of $\Psi$ is not only conserved but is also non-negative.