Eigenvalue Problem of Scalar Fields in BTZ Black Hole Spacetime

Kuwata, Maiko; Kenmoku, Masakatsu; Shigemoto, Kazuyasu

Eigenvalue Problem of Scalar Fields in BTZ Black Hole Spacetime

Authors

Kuwata, Maiko

Kenmoku, Masakatsu

Shigemoto, Kazuyasu

Description

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