Normal Modes and No Zero Mode Theorem of Scalar Fields in BTZ Black Hole Spacetime

TL;DR

This paper analyzes scalar field normal modes in BTZ black hole spacetime, deriving orthonormal relations, quantization, and exploring the no zero mode theorem's implications for statistical mechanics.

Contribution

It introduces the no zero mode theorem for scalar fields in BTZ spacetime and examines its impact on mode quantization and statistical mechanics.

Findings

Derived orthonormal relations for scalar modes.

Established the no zero mode theorem in BTZ spacetime.

Explored implications for black hole thermodynamics.

Abstract

Eigenfunctions for normal modes of scalar fields in BTZ black hole spacetime are studied. Orthonormal relations among them are derived. Quantization for scalar fields is done and particle number, energy and angular momentum are expressed by the creation and annihilation operators. Allowed physical normal mode region is studied on the basis of the no zero mode theorem. Its implication to the statistical mechanics is also studied.