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• W3205673996 abstract "We study the free data in the Fefferman-Graham expansion of asymptotically Einstein metrics with non-zero cosmological constant. We prove that if $mathscr{I}$ is conformally flat, the rescaled Weyl tensor at $mathscr{I}$ agrees up to a constant with the free data at $mathscr{I}$ , namely the traceless part of the $n$-th order coefficient of the expansion. In the non-conformally flat case, the rescaled Weyl tensor is generically divergent at $mathscr{I}$ but one can still extract the free data in terms of the difference of the Weyl tensors of suitably constructed metrics, in full generality when the spacetime dimension $D$ is even and provided the so-called obstruction tensor at $mathscr{I}$ is identically zero when $D$ is odd. These results provide a geometric definition of the data, particularly relevant for the asymptotic Cauchy problem of even dimensional Einstein metrics with positive $Lambda$ and also for the odd dimensional analytic case irrespectively of the sign of $Lambda$. We establish a Killing initial data equation at spacelike $mathscr{I}$ in all dimension for analytic data. These results are used to find a geometric characterization of the Kerr-de Sitter metrics in all dimensions in terms of its geometric data at null infinity." @default.
• W3205673996 created "2021-10-25" @default.
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• W3205673996 date "2021-10-01" @default.
• W3205673996 modified "2023-10-14" @default.
• W3205673996 title "Free data at spacelike $${mathscr {I}}$$ and characterization of Kerr-de Sitter in all dimensions" @default.
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• W3205673996 doi "https://doi.org/10.1140/epjc/s10052-021-09704-6" @default.
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