Raychaudhuri Focusing in Causal Open-System Gravity

We develop a covariant open-system effective theory of a resolved spacetime sector and use it to obtain a local obstruction of Raychaudhuri focusing. The construction treats the resolved gravitational sector as an open subsystem in the sense of nonequilibrium effective field theory: its fundamental data are a closed-time-path coarse-grained effective action and an admissible pair of retarded response and symmetric noise kernels. Classical general relativity, semiclassical gravity, and Einstein-Langevin stochastic gravity arise as nested statistical closures of the same kernel-defined theory, while Israel-Stewart-type transport equations appear as local finite-relaxation truncations of an underlying nonlocal constitutive response. Applying this structure to spherically symmetric stellar-core collapse, we derive a conditional local obstruction criterion for the Raychaudhuri focusing estimate. The Raychaudhuri equation is rewritten in terms of an obstruction functional containing acceleration divergence, anisotropic stress, finite-relaxation transport, and stochastic backreaction. On collapsing segments where this functional satisfies explicit local bounds, the classical quadratic estimate driving the expansion scalar to negative infinity is replaced by a linear lower bound. In the open-system closure, rapid compression drives dissipative stresses out of equilibrium; when the stress-variation length is bounded by the causal transport scale, the outward acceleration-divergence contribution scales at the same order as the classical quadratic compression term. The result is local, conditional, and constitutive: it obstructs the Raychaudhuri blow-up estimate inside the resolved effective theory. It does not by itself prove global geodesic completeness, absence of trapped surfaces, boundedness of all curvature invariants, or almost-sure stochastic regularity; those require additional global, analytic, and probabilistic hypotheses. A reduced strong-field model illustrates the same mechanism as a short-distance transport barrier in the collective core radius. This construction is the gravitational sector of a broader open-system program for spacetime physics; the present paper develops only the gravitational backbone needed for the local Raychaudhuri-obstruction result, and is self-contained.