Cvetič M, Gibbons G W, Pope C N, Whiting B F
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI2000 Maribor, Slovenia.
Phys Rev Lett. 2020 Jun 12;124(23):231102. doi: 10.1103/PhysRevLett.124.231102.
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.
我们概述了在一大类四维渐近平直旋转且“带电”的超引力解以及弦理论的低能极限（即STU度规）背景下，无质量中性标量场ψ稳定性的证明。尽管这些度规很复杂，但我们发现可以通过采用惠廷提出的策略来规避原始度规中存在能层区域以及相关的超辐射现象所带来的困难，即过渡到一个允许处处为类光的Killing场的辅助度规，并构造一个标量场ψ（通过非局部变换与可能的不稳定模式ψ相关），该标量场相对于辅助度规满足无质量波动方程。与ψ的情况不同，ψ的相关能量密度不仅守恒，而且是非负的。
