Spin field equations and Heun’s equations
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The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We study the separability of the equations of the massless scalar (spin s=0), neutrino (s=1/2), electromagnetic (s=1), Rarita-Schwinger (s=3/2), and gravitational (s=2) fields propagating on this background. We obtain the angular and radial master equations, and show that the master equations are transformed to Heun’s equation. Meanwhile, we give the condition of existence of event horizons for Kerr-Newman-(anti) de Sitter spacetime by using Sturm theorem.
KeywordsBlack holes Spin fields Heun’s equation
This work was supported by NSFC Grant Nos. 11475148, 11075141, 11173021 and 11305140.