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The instability of rotating Kerr black holes due to massive scalarperturbations is investigated. It is well known that a bosonic field impingingon a Kerr black hole can be amplified as it scatters off the hole. Thissuperradiant scattering occurs for frequencies in the range $\omega<m\Omega$,where $\Omega$ is the angular frequency of the black hole and $m$ is theazimuthal harmonic index of the mode. If the incident field has a non-zero restmass, $\mu$, then the mass term effectively works as a mirror, reflecting thescattered wave back towards the black hole. The wave may bounce back and forthbetween the black hole and some turning point amplifying itself each time. Thismay lead to a dynamical instability of the system, a phenomena known as a"black-hole bomb". In this work we provide a bound on the instability regime ofrotating Kerr spacetimes. In particular, we show that Kerr black holes arestable to massive perturbations in the regime $\mu\geq\sqrt{2}m\Omega$.

On the instability regime of the rotating Kerr spacetime to massive scalar perturbations