Energy bounds and ergoregion instability in Einstein-Maxwell-Scalar field models
Filipe C. Mena, João M. Oliveira
TL;DR
The paper investigates energy bounds and ergoregion instability in Einstein-Maxwell-Scalar (EMS) theories by treating a non-minimally coupled scalar perturbation on a stationary, asymptotically flat EM background. It constructs energy functionals incorporating EMS couplings and proves the existence of compactly supported initial data with negative initial $T$-energy flux, showing the flux does not decay and, via Friedman–Moschidis arguments, diverges at future null infinity. This establishes ergoregion instability in horizonless EMS spacetimes and identifies conditions under which instability arises, including generalizations to derivative couplings. The results motivate further nonlinear analysis and numerical studies in beyond-GR models with scalar–electromagnetic couplings, and raise questions about the role of coupling divergences in stabilizing ergoregions.
Abstract
We investigate energy bounds and the stability of stationary asymptotically flat spacetimes with an ergoregion and no future horizon in the context of Einstein-Maxwell-Scalar field models which naturally arise in Kaluza-Klein and String theories. In order to do that we consider scalar field perturbations non-minimally coupled to a background electromagnetic field. We show that there is compactly supported initial data such that the initial energy flux across the initial Cauchy hypersurface is negative and that the energy flux decreases with time. Then, considering arguments due to J. Friedman and G. Moschidis, this indicates that the energy flux diverges for those solutions and such spacetimes with an ergoregion are unstable.