Exact Solutions of Teukolsky Master Equation with Continuous Spectrum

Understand

Weak gravitational, electromagnetic, neutrino and scalar fields, considered as perturbations on Kerr background satisfy Teukolsky Master Equation.

• The two non-trivial equations obtained after separating the variables are the polar angle equation and the radial equation.
• We solve them by transforming each one into the form of a confluent Heun equation.
• The transformation depends on a set of parameters, which can be chosen in a such a way, so the resulting equations have simple polynomial solutions for neutrino, electromagnetic, and gravitational perturbations, provided some additional conditions are satisfied.