Quantisation of Conformal Fields in Three-dimensional Anti-de Sitter Black Hole Spacetime

TL;DR

This paper explicitly quantizes conformally-coupled scalar and spinor fields in the AdS_3 black hole spacetime, demonstrating the absence of particle production and superradiance due to conformal triviality.

Contribution

It provides explicit mode expansions and propagators for these fields in AdS_3 black hole background, establishing the absence of particle creation and superradiance.

Findings

Vacuum is the conformal vacuum with global meaning.

No particle production occurs in this spacetime.

Superradiance is absent for conformally-coupled fields.

Abstract

Utilizing the conformal-flatness nature of 3-dim. Anti-de Sitter (AdS_3) black hole solution of Banados, Teitelboim and Zanelli, the quantisation of conformally-coupled scalar and spinor fields in this background spacetime is explicitly carried out. In particular, mode expansion forms and propagators of the fields are obtained in closed forms. The vacuum in this conformally-coupled field theories in AdS_3 black hole spacetime, which is conformally-flat, is the conformal vacuum which is unique and has global meaning. This point particularly suggests that now the particle production by AdS_3 black hole spacetime should be absent. General argument establishing the absence of real particle creation by AdS_3 black hole spacetime for this case of conformal triviality is provided. Then next, using the explicit mode expansion forms for conformally-coupled scalar and spinor fields, the bosonic and fermionic superradiances are examined and found to be absent confirming the expectation.