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In recent years, there has been considerable interest in theories formulatedin anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globallyhyperbolic, so a classical field satisfying a hyperbolic wave equation on AdSspacetime need not have a well defined dynamics. Nevertheless, AdS spacetime isstatic, so the possible rules of dynamics for a field satisfying a linear waveequation are constrained by our previous general analysis--given in paperII--where it was shown that the possible choices of dynamics correspond tochoices of positive, self-adjoint extensions of a certain differentialoperator, $A$. In the present paper, we reduce the analysis of electromagnetic,and gravitational perturbations in AdS spacetime to scalar wave equations. Wethen apply our general results to analyse the possible dynamics of scalar,electromagnetic, and gravitational perturbations in AdS spacetime. In AdSspacetime, the freedom (if any) in choosing self-adjoint extensions of $A$corresponds to the freedom (if any) in choosing suitable boundary conditions atinfinity, so our analysis determines all of the possible boundary conditionsthat can be imposed at infinity. In particular, we show that other boundaryconditions 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 forelectromagnetic and gravitational perturbations.Comment: 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. Gra

Dynamics in non-globally-hyperbolic static spacetimes: III. Anti-de Sitter spacetime