Entanglement Stars: Self-consistent Schwarzschild exterior from entanglement closure on quantum lattice

Quantum correlations between neighboring sites of a lattice behave like conductances in a resistor network. We show that when a localized energy defect is placed on the lattice, the conductances define a geometry that can be made mutually consistent with the quantum state. In spherical symmetry this self-consistency produces an unscreened $1/r$ far-field gravitational potential whose strength sets the mass. Because the conductances scale as the squared lapse ($N^2$), the closure equation reduces to Laplace's equation whose solution is exactly the radial co-metric, and the exterior takes the Schwarzschild form including the post-Newtonian expansion. We refer to the resulting object as an \emph{entanglement star}, supported by conductances that play the role of an effective degeneracy pressure. The lapse remains strictly positive because conductances are suppressed before the lapse reaches zero, replacing the classical singularity by a conical interior geometry within the model. Tracking mode-by-mode evaporation in the unitary Gaussian state, the radiation entropy exhibits a Page-like curve. Within the closure framework we derive expressions corresponding to surface gravity, Hawking temperature, and the first law. Self-consistent numerical calculations validate key analytic results for free fermions, an interacting XXZ chain, and a 3D cubic lattice. Replacing the defect with a Tolman-Klein equilibrium gives a self-consistent stellar interior, whose astrophysical limit leads to gravitationally relevant entanglement concentrated at the Schwarzschild radius.