Constitutive invariants for the rotating pseudo-complex Kerr solution

Identify the additional transverse constitutive invariants required for the rotating pseudo-complex Kerr solution and determine to what extent their constitutive dependence can be reconstructed from the known rotating vacuum sector.

Background

For the static pseudo-complex Schwarzschild solution, spherical symmetry restricts the constitutive response to the isotropic trace sector, allowing the authors to reconstruct a logarithmic-strain potential. The rotating pseudo-complex Kerr solution introduces additional rotational dependence that the static trace-sector law cannot capture. The paper suggests that invariants associated with the traceless transverse shear sector may provide the needed extension, but the known rotating solution does not determine their form or constitutive dependence.