Energy bounds and ergoregion instability in Einstein-Maxwell-Scalar field models

TL;DR

This paper analyzes the stability of certain Einstein-Maxwell-Scalar spacetimes with ergoregions, demonstrating that specific initial conditions lead to energy divergence and instability, highlighting potential issues in these models.

Contribution

It introduces a method to show that spacetimes with ergoregions in Einstein-Maxwell-Scalar models are unstable due to negative energy fluxes and divergence over time.

Findings

Existence of initial data with negative energy flux

Energy flux decreases initially but diverges over time

Spacetimes with ergoregions are unstable under scalar perturbations

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.