A covariant Moore-Penrose algorithm for complex degenerate metrics is formulated, but its uniqueness and torsion interpretation depend on an arbitrary auxiliary metric and the central proof is incomplete.
Matter coupling to degenerate spacetimes in first order gravity
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We develop a systematic study of the equations of motion in the first order gravity with matter fields for degenerate metrics. Like the Hilbert-Palatini action functional for pure gravity, the action functionals for matter fields used are first order. These are defined for both invertible and non- invertible metrics. Description for invertible metrics is equivalent to second order gravity theory with matter. For degenerate metrics the theory describes a different phase. The analysis for tetrads with one zero eigen value in theory with scalar, Abelian vector gauge and fermion matter fields is presented in detail.
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Complex degenerate metrics in general relativity: a covariant extension of the Moore-Penrose algorithm
A covariant Moore-Penrose algorithm for complex degenerate metrics is formulated, but its uniqueness and torsion interpretation depend on an arbitrary auxiliary metric and the central proof is incomplete.