Numerical aspects of black hole superradiance

TL;DR

This paper develops a versatile numerical method using spherical harmonics and Chebyshev interpolation to compute quasi-bound states of perturbations in spinning black holes, aiding the study of superradiant instabilities and testing theories beyond General Relativity.

Contribution

It introduces a separation-ansatz-independent numerical technique applicable to scalar, vector, and tensor perturbations in black hole spacetimes, including non-linear scalar-tensor theories.

Findings

Effective computation of scalar and vector quasi-bound states.

Extension to tensor perturbations without known separability.

Application to scalar-tensor theories with plasma interactions.

Abstract

In this work we explore a numerical technique, based on the spherical harmonic decomposition and the discretization of the radial coordinate through \v{C}eby\v{s}\"ev 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 ans\"atze, 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 massless scalar perturbations acquires an effective mass, finding a novel way for constraining scalar-tensor theories.