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- W3118746571 abstract "We discuss dynamics of massive Klein-Gordon fields in two-dimensional anti-de Sitter spacetimes (${mathrm{AdS}}_{2}$), in particular conserved quantities and nonmodal instability on the future Poincar'e horizon called, respectively, the Aretakis constants and the Aretakis instability. We find out the geometrical meaning of the Aretakis constants and instability in a parallel-transported frame along a null geodesic; i.e., some components of the higher-order covariant derivatives of the field in the parallel-transported frame are constant or unbounded at the late time. Because ${mathrm{AdS}}_{2}$ is maximally symmetric, any null hypersurfaces have the same geometrical properties. Thus, if we prepare parallel-transported frames along any null hypersurfaces, we can show that the same instability emerges not only on the future Poincar'e horizon but also on any null hypersurfaces. This implies that the Aretakis instability in ${mathrm{AdS}}_{2}$ is the result of singular behaviors of the higher-order covariant derivatives of the fields on the whole AdS infinity, rather than a blowup on a specific null hypersurface. It is also discussed that the Aretakis constants and instability are related to the conformal Killing tensors. We further explicitly demonstrate that the Aretakis constants can be derived from ladder operators constructed from the spacetime conformal symmetry." @default.
- W3118746571 created "2021-01-18" @default.
- W3118746571 creator A5002302795 @default.
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- W3118746571 date "2021-03-08" @default.
- W3118746571 modified "2023-09-23" @default.
- W3118746571 title "Revisiting the Aretakis constants and instability in two-dimensional anti–de Sitter spacetimes" @default.
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- W3118746571 doi "https://doi.org/10.1103/physrevd.103.064011" @default.
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