# metadata.dc.description[].value
Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2017, Tutor: Helvi Witek

# metadata.dc.description.abstract[].value
We solve the Klein-Gordon equation for an axion field in a Kerr background analytically for M [mu] << 1 and M [omega] << 1 for small spins via matching the near and far region solutions. This yields a hydrogen-like frequency spectrum and, if the superradiance condition is met, an instability. Moreover, we discuss some physically relevant elements of our system such as the potential associated to a black hole, the superradiance rate or the flux at the event horizon, comparing them with the numerical solution where our approximations are no longer valid.