Higher fundamental forms of the conformal boundary of asymptotically de Sitter spacetimes. (English) Zbl 1516.83012
Summary: We provide a partial characterization of the conformal infinity of asymptotically de Sitter spacetimes by deriving constraints that relate the asymptotics of the stress-energy tensor with conformal geometric data. The latter is captured using recently defined objects, called higher conformal fundamental forms. For the boundary hypersurface, these generalize to higher order the trace-free part of the second form.
MSC:
| 83C30 | Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory |
| 53C18 | Conformal structures on manifolds |
| 70H45 | Constrained dynamics, Dirac’s theory of constraints |
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