Astrophysics II: Reference-System Transitions and Scale-Dependent Causal Dynamics in General Relativity

Abstract The companion paper develops the causal dynamics of the retarded geometric residual. We study the complementary problem of how this residual changes when the physical reference system is enlarged. At scale \(L\), the system is specified by \[ \mathfrak R_L=(\gamma_L,e_{(a)}{}^\mu,\Omega_L,\mathscr P_L,\mathcal O_L). \] This formulation separates coordinate changes from changes of observer, domain, retained degrees of freedom, boundary conditions, source support, and selected physical quantities. We prove that diffeomorphisms preserve curvature, relative-motion, and optical predictions, whereas a physical transition can change the field components included in the description. In a normal Fermi tube, a smooth external acceleration cancels from relative motion, while its Hessian remains as a tidal term. For a solar-centered system, we obtain \[ \frac{\|\delta a_{\rm SS}\|}{\|a_\odot\|} \leq C\left( \varepsilon_{\rm mass} +\varepsilon_{\rm GR} +\varepsilon_{\rm tide} +\varepsilon_{\rm corr} +\varepsilon_{\rm tail} \right). \] For a normally hyperbolic gauge-fixed Einstein equation, we represent the field by a retarded history integral over \(J^-(x)\). Enlarging a finite physical domain from \(L_1\) to \(L_2\) gives the exact source-shell increment \[ H^{(L_2)}-H^{(L_1)} = G^+\!\left[(\chi_{L_2}-\chi_{L_1})S\right]. \] Under an explicit compensator hypothesis, we also establish conservative source restriction, nonlinear Volterra–Duhamel well-posedness, and a coarea formula for the scale derivative. Nested reference systems restore center variables and their covariance shell, which can contribute to the established zero-frequency response. Finally, we define a geometric response factor, prove its coordinate invariance and continuity in the physical fields and parameters, and show that local suppression is compatible with a nonzero collective response on a larger dynamical domain. Keywords General relativity; physical reference systems; Fermi normal coordinates; retarded Green functions; galactic dynamics; tidal suppression; scale-dependent response.