Dynamics in nongloballyhyperbolic static spacetimes: III. Antide Sitter spacetime
Abstract
In recent years, there has been considerable interest in theories formulated in antide Sitter (AdS) spacetime. However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS spacetime need not have a welldefined dynamics. Nevertheless, AdS spacetime is static, so the possible rules of dynamics for a field satisfying a linear wave equation are constrained by our previous general analysis—given in paper II—where it was shown that the possible choices of dynamics correspond to choices of positive, selfadjoint extensions of a certain differential operator, A. In the present paper, we reduce the analysis of electromagnetic and gravitational perturbations in AdS spacetime to scalar wave equations. We then apply our general results to analyse the possible dynamics of scalar, electromagnetic and gravitational perturbations in AdS spacetime. In AdS spacetime, the freedom (if any) in choosing selfadjoint extensions of A corresponds to the freedom (if any) in choosing suitable boundary conditions at infinity, so our analysis determines all the possible boundary conditions that can be imposed at infinity. In particular, we show that other boundary conditions besides the Dirichlet and Neumann conditions may be possible, depending on the value of the effective mass for scalar field perturbations, and depending on the number of spacetime dimensions and type of mode for electromagnetic and gravitational perturbations.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 June 2004
 DOI:
 10.1088/02649381/21/12/012
 arXiv:
 arXiv:hepth/0402184
 Bibcode:
 2004CQGra..21.2981I
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 43 pages, no figures, references and comments on the case of more general bulk geometries are added, minor corrections, discussion on the case of black holes with a generic Einstein horizon manifold is removed, to appear in Class. Quant. Grav