Zero, Normal and Super-radiant Modes for Scalar and Spinor Fields in Kerr-anti de Sitter Spacetime

TL;DR

This paper investigates the existence and properties of zero, normal, and super-radiant modes for scalar and spinor fields in Kerr-anti de Sitter spacetime, revealing the non-existence of zero modes and conditions for normal modes.

Contribution

It demonstrates that zero modes do not exist as physical states and clarifies the spectrum condition for normal modes in Kerr-anti de Sitter spacetime.

Findings

Zero modes are not physical states for scalar and spinor fields.

Normal modes satisfy the condition p_H > 0 due to spectrum constraints.

Comments on super-radiant modes and black hole thermodynamics are provided.

Abstract

Zero and normal modes for scalar and spinor fields in Kerr-anti de Sitter spacetime are studied as bound state problem with Dirichlet and Neumann boundary conditions. Zero mode is defined as the momentum near the horizon to be zero: $p_{\rm H}=\omega-\Omega_{\rm H}m=0$, and is shown not to exist as physical state for both scalar and spinor fields. Physical normal modes satisfy the spectrum condition $p_{\rm H}>0$ as a result of non-existence of zero mode and the analyticity with respect to rotation parameter $a$ of Kerr-anti de Sitter black hole. Comments on the super-radiant modes and the thermodynamics of black hole are given in relation to the spectrum condition for normal modes. Preliminary numerical analysis on normal modes is presented.