Free data at spacelike $\mathscr{I}$ and characterization of Kerr-de Sitter in all dimensions
| Autor: | Marc Mars, Carlos Peón-Nieto |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Weyl tensor
Physics Pure mathematics Physics and Astronomy (miscellaneous) Physical constant Null (mathematics) Dimension (graph theory) Order (ring theory) FOS: Physical sciences QC770-798 General Relativity and Quantum Cosmology (gr-qc) Mathematical Physics (math-ph) Astrophysics General Relativity and Quantum Cosmology QB460-466 symbols.namesake De Sitter universe Nuclear and particle physics. Atomic energy. Radioactivity Homogeneous space symbols Mathematics::Representation Theory Engineering (miscellaneous) Mathematical Physics Flatness (mathematics) |
| Zdroj: | European Physical Journal European Physical Journal C: Particles and Fields, Vol 81, Iss 10, Pp 1-22 (2021) |
| Popis: | 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. Comment: 25 pages, matches published version |
| Databáze: | OpenAIRE |
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