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

M. Cvetič, G. W. Gibbons, C. N. Pope, and B. F. Whiting

Phys. Rev. Lett. 124, 231102 – Published 12 June 2020

Abstract

We outline a proof of the stability of a massless neutral scalar field $ψ$ 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 superradiance 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 $ψ$ (related to a possible unstable mode $ψ$ by a nonlocal transformation) which satisfies the massless wave equation with respect to the auxiliary metric. By contrast with the case for $ψ$ , the associated energy density of $ψ$ is not only conserved but is also non-negative.

Received 9 January 2020
Revised 2 March 2020
Accepted 1 June 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.231102

Physics Subject Headings (PhySH)

Classical black holes General relativity General relativity equations & solutions

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

M. Cvetič^1,2, G. W. Gibbons ³, C. N. Pope ^4,3, and B. F. Whiting ⁵

¹Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
²Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI2000 Maribor, Slovenia
³DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
⁴George P. & Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
⁵Department of Physics, University of Florida, Post Office Box 118440, Gainesville, Florida 32611-8440, USA