Constitutive Geometry of the Effective Vacuum Sector of Pseudo-Complex General Relativity

@misc{weber2026constitutive,
  title = {{Constitutive Geometry of the Effective Vacuum Sector of Pseudo-Complex General Relativity}},
  author = {F. Weber and P. O. Hess and C. A. Zen Vasconcellos},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10836},
  eprint = {2610.10836},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10836},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Constitutive Geometry of the Effective Vacuum Sector of Pseudo-Complex General Relativity
AU  - F. Weber
AU  - P. O. Hess
AU  - C. A. Zen Vasconcellos
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10836
UR  - https://arxiv.org/abs/2610.10836
AB  - Effective vacuum sectors in modified theories of gravity are often represented by anisotropic stress-energy tensors, even when the underlying source is geometric rather than material. This raises a broader question: can such effective stresses be characterized intrinsically through a covariant constitutive structure, rather than modeled phenomenologically as exotic fluids? We address this question in pseudo-complex general relativity (pcGR), where a constrained variational formulation identifies the effective vacuum source as geometric in origin but does not uniquely determine the corresponding geometric constraint sector. For the static pseudo-complex Schwarzschild solution, we show that the effective vacuum tensor separates naturally into an isotropic contribution and a purely transverse contribution associated with the intrinsic geometry of the two-dimensional subspace orthogonal to the timelike and radial directions. This decomposition leads to a constitutive formulation based on the transverse metric. Its infinitesimal deformations split uniquely into trace and traceless shear modes, with the static solution having only an isotropic transverse response. Within the class of local constitutive variables that depend algebraically on the transverse metric and whose first variation generates the trace projector with stateindependent normalization, the logarithmic transverse area strain is the minimal scalar constitutive coordinate.
ER  -