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- W1991362861 abstract "In the present paper a global conformal invariant $Y$ of a closed initial data set is constructed. A spacelike hypersurface $Sigma$ in a Lorentzian spacetime naturally inherits from the spacetime metric a differentiation ${cal D}_e$, the so-called real Sen connection, which turns out to be determined completely by the initial data $h_{ab}$ and $chi_{ab}$ induced on $Sigma$, and coincides, in the case of vanishing second fundamental form $chi_{ab}$, with the Levi-Civita covariant derivation $D_e$ of the induced metric $h_{ab}$. $Y$ is built from the real Sen connection ${cal D}_e$ in the similar way as the standard Chern-Simons invariant is built from $D_e$. The number $Y$ is invariant with respect to changes of $h_{ab}$ and $chi_{ab}$ corresponding to conformal rescalings of the spacetime metric. In contrast the quantity $Y$ built from the complex Ashtekar connection is not invariant in this sense. The critical points of our $Y$ are precisely the initial data sets which are locally imbeddable into conformal Minkowski space." @default.
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- W1991362861 date "1997-11-01" @default.
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- W1991362861 title "On a global conformal invariant of initial data sets" @default.
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- W1991362861 doi "https://doi.org/10.1088/0264-9381/14/11/010" @default.
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