The Dirac equation in Kerr–Newman–Ads black hole background

Abstract

We consider the Dirac equation on the Kerr–Newman–AdS black hole background. We first perform the variable separation for the Dirac equation and define the Hamiltonian operator Ĥ. Then we show that for a massive Dirac field with mass μ≥1/(2l), where l is linked to the cosmological constant Λ by Λ≕−3/l2, essential self-adjointness of Ĥ on C0∞((r+,∞)×S2)4 is obtained even in presence of the boundarylike behavior of infinity in an asymptotically AdS black hole background. Furthermore, qualitative spectral properties of the Hamiltonian are taken into account and in agreement with the existing results concerning the case of stationary axisymmetric asymptotically flat black holes we infer the absence of time-periodic and normalizable solutions of the Dirac equation around the black hole in the nonextremal case.