Variational Origin of the Absence Tensor in Causal General Relativity (CGR)

This technical note derives the Absence Tensor within the framework of Causal General Relativity (CGR) from a fully covariant variational principle. A scalar absence field is introduced and minimally coupled to spacetime geometry, showing that the resulting tensorial contribution arises dynamically from the action rather than being postulated at the level of field equations. Diffeomorphism invariance guarantees conservation laws, and the Einstein limit is recovered in the regime of vanishing absence. This work provides the variational closure of the absence sector and serves as a technical precursor to the foundational treatise Causal General Relativity (CGR): Treatise on Absence and Orthogonality.