Eigenvalue Problem of Scalar Fields in BTZ Black Hole Spacetime

Abstract

We studied the eigenvalue problem of scalar fields in the (2+1)-dimensional BTZ black hole spacetime. The Dirichlet boundary condition at infinity and the Dirichlet or the Neumann boundary condition at the horizon are imposed. Eigenvalues for normal modes are characterized by the principal quantum number $(0<n)$ and the azimuthal quantum number $(-\infty <m<\infty )$. Effects to eigenvalues of the black hole rotation and of the scalar field mass are studied explicitly. Relation of the black hole rotation to the super-radiant instability is discussed.

10 pages, 6 figures

References in corpus (4)

• Entropies of Scalar Fields on Three Dimensional Black Holes
• Entropy of the BTZ Black Hole in 2+1 Dimensions
• Superradiance and the Statistical-Mechanical Entropy of Rotating BTZ Black Holes
• Black Holes, Holography and Moduli Space Metric

Cited by in corpus (9)

• Normal Modes and No Zero Mode Theorem of Scalar Fields in BTZ Black Hole Spacetime
• Scalar field dynamics in warped AdS_3 black hole background
• Quasinormal modes of charged BTZ black holes
• Normal mode analysis for scalar fields in BTZ black hole background
• Quantum space and quantum completeness
• Aspects of the BTZ black hole interacting with fields
• Bargmann-Wigner Formulation and Superradiance Problem of Bosons and Fermions in Kerr Space-time
• Zero, Normal and Super-radiant Modes for Scalar and Spinor Fields in Kerr-anti de Sitter Spacetime
• Spectral Bifurcations in Quasinormal Modes of Regular BTZ Black Holes