A proof of Friedman's ergosphere instability for scalar waves

Understand

Let $(\mathcal{M}^{3+1},g)$ be a real analytic, stationary and asymptotically flat spacetime with a non-empty ergoregion $\mathscr{E}$ and no future event horizon $\mathcal{H}^{+}$.

• On such spacetimes, Friedman provided a heuristic argument that the energy of certain solutions $\phi$ of $\square_{g}\phi=0$ grows to $+\infty$ as time increases.
• In this paper, we provide a rigorous proof of Friedman's instability.
• Our setting is, in fact, more general.