Thesis title: Numerical aspects of black hole superradiance
In this work we explore a numerical technique, based on the spherical harmonic
decomposition and the discretization of the radial coordinate through Čebyšëv polynomial
interpolation, for the computation of quasi-bound states of linear massive
scalar and vector perturbations in spinning black hole spacetimes in General Relativity.
The aim is studying black hole superradiant instabilities, an energy-extraction
mechanism triggered by the presence of massive bosonic fields near black holes, which
finds wide applications in constraining scenarios beyond Standard Model and General
Relativity. This method does not rely on any separation ansätze, thus it can have
wide applications. Consequently we extend the technique so that it can be applied
also to the computation of massive tensor quasi-bound states in spinning black
holes in General Relativity, whose separability ansatz is currently unknown. We
also apply it to spinning black holes in scalar-tensor theory non-linearly interacting
with plasma, wherein the mass-less scalar perturbations acquires an effective mass,
finding a novel way for constraining scalar-tensor theories.