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.