Dynamics in non-globally-hyperbolic static spacetimes: III. Anti-de Sitter spacetime
By A. Ishibashi, R. Wald. 2004
270 citations recorded by the source corpus.
In recent years, there has been considerable interest in theories formulated in anti-de 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 well-defined 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, self-adjoint 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 self-adjoint 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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/0dff30d04c62be23ecf449ac2c335ca7aef00509
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Citations in the corpus
- Boundary conditions and dualities: vector fields in AdS/CFT (2006, methodology): “In a recent thorough analysis by Ishibashi and Wald [14], it was shown that for electromagnetic and gravitational perturbations in AdS spacetime, both the slowand fast- falloff pieces of certain parts of the field are normalizable for d = 3, 4, 5; i.”
- Comparison between various notions of conserved charges in asymptotically AdS spacetimes (2005, background): “Some properties of these tensor harmonics and decomposition theorems are given in [ 43 , 61].”