Researchers have investigated the critical regime in $κ(R,T)$ gravity theory, where the effective gravitational coupling $κ$ vanishes. Unlike most studies that assume a non-zero coupling, the existence of these critical hypersurfaces is an inherent feature of many admissible coupling functions in this theory. The study reveals that an apparent singularity in the non-conservation equation is, in fact, an artifact of a rewritten form of the conservation law, and that the fundamental equations of the theory remain regular even when $κ=0$.

Further analysis delves into the structure of these critical hypersurfaces, deriving the associated compatibility condition, $(\nabla^μκ)T_{μν}=0$. These surfaces are interpreted as gravitational screening surfaces that delineate attractive and repulsive gravitational phases. This finding is crucial, as the existence of these critical coupling surfaces obstructs a global Einstein-frame description, distinguishing $κ(R,T)$ gravity from other theories based solely on algebraic redefinitions of the energy-momentum tensor.

The implications of these critical surfaces are significant for cosmology and astrophysics. The ability of gravity to switch from attractive to repulsive in certain regions could offer new insights into phenomena such as the accelerated expansion of the universe or large-scale structure formation. Although the study only briefly explores these consequences, it lays the groundwork for future research into how these gravitational phase transitions might manifest in the observable universe.