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The classical notion of manifold may be augmented to institute the algebrasassociated with the generators of the spinor and vector representations of theLorentz group on two copies of the cotangent space. In the former case, thisresults in the emergence of a Dirac operator out of the vacuum of GeneralRelativity. In the backdrop of the Higgs VEV, a volume form with such a dualcharacter endows the augmented manifold with dark matter content as thesimplest conceivable geometric structure that could emerge out of the unifiedvacuum.

On the Vacua of General Relativity in the Backdrop of the Higgs VEV