Curvture Regularization and Dynamical Vacuum Structure in Pseudo-Complex General Relativity
Abstract
Whether classical spacetime remains welldefined at arbitrarily high curvature is a central question. In general relativity, singularities signal the breakdown of the classical description, motivating modifications of spacetime's short-distance structure. Pseudocomplex general relativity (pcGR) extends spacetime geometry to pseudo-complex coordinates, naturally introducing two metric sectors, the physical metric gμν and an auxiliary field fμν. The magnitude of the pseudo imaginary component defines the invariant acceleration scale a0, a direct consequence of the pseudo-complex structure. The simultaneity condition, requiring both idempotent sectors to satisfy the pseudo-complex Einstein equations independently, fixes the auxiliary field algebraically, with no new propagating degrees of freedom, and sets a lower bound on the lapse that regularizes curvature. The regularization is achieved through the combined effect of the lapse-gap condition eν(r) gt. a0, which ensures the radial metric component remains nondegenerate, together with the regularity conditions at the areal-radius origin, B(0) = 1 and B'(0) = 0, which emerge naturally from the pseudo-complex geometry. These conditions jointly eliminate the Schwarzschildtype curvature divergence, rather than the gap condition acting alone.
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BibTeX
@misc{weber2026curvture,
title = {{Curvture Regularization and Dynamical Vacuum Structure in Pseudo-Complex General Relativity}},
author = {Fridolin Weber and Peter Otto Hess and Cesar Augusto Zen Vasconcellos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15916},
eprint = {2609.15916},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15916},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Curvture Regularization and Dynamical Vacuum Structure in Pseudo-Complex General Relativity
AU - Fridolin Weber
AU - Peter Otto Hess
AU - Cesar Augusto Zen Vasconcellos
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15916
UR - https://arxiv.org/abs/2609.15916
AB - Whether classical spacetime remains welldefined at arbitrarily high curvature is a central question. In general relativity, singularities signal the breakdown of the classical description, motivating modifications of spacetime's short-distance structure. Pseudocomplex general relativity (pcGR) extends spacetime geometry to pseudo-complex coordinates, naturally introducing two metric sectors, the physical metric gμν and an auxiliary field fμν. The magnitude of the pseudo imaginary component defines the invariant acceleration scale a0, a direct consequence of the pseudo-complex structure. The simultaneity condition, requiring both idempotent sectors to satisfy the pseudo-complex Einstein equations independently, fixes the auxiliary field algebraically, with no new propagating degrees of freedom, and sets a lower bound on the lapse that regularizes curvature. The regularization is achieved through the combined effect of the lapse-gap condition eν(r) gt. a0, which ensures the radial metric component remains nondegenerate, together with the regularity conditions at the areal-radius origin, B(0) = 1 and B'(0) = 0, which emerge naturally from the pseudo-complex geometry. These conditions jointly eliminate the Schwarzschildtype curvature divergence, rather than the gap condition acting alone.
ER -