Emergent Gravity via Causal Smoothing of the Vacuum Substrate

Abstract — Revised Version This revised version develops a covariant effective framework for Emergent Gravity via Causal Smoothing of the Vacuum Substrate, extending the original formulation with additional phenomenological and strong-field analyses. The theory models macroscopic gravity as a causal collective response of microscopic Vacuum Substrate degrees of freedom and introduces a nonlinear curvature-response relation characterized by the asymptotic scale Rₘₐₓ. The revised manuscript strengthens the cosmological and gravitational-wave sectors through updated scalar and tensor perturbation analyses, including post-Newtonian constraints, gravitational-wave friction, and the relation between gravitational-wave and electromagnetic luminosity distances. The strong-field analysis is further developed through horizon conditions, asymptotic Schwarzschild matching, regular-center expansions, and the resulting no-hair constraint on the present scalar-tensor sector. A major new component is the relativistic neutron-star/TOV boundary-value analysis. An Einstein-frame stellar system is derived and solved in linear scalar response for a representative Γ = 2, K = 100 relativistic polytropic equation of state. The resulting mass-radius sequence provides a first calculation of the compact-object scalar response, α_A(m_A) = S_A(m_A)α_∞, where S_A measures strong-field amplification of the asymptotic scalar coupling. The analysis finds no linear spontaneous-scalarization instability for the present β_DEF ≃ -2 coupling in the representative sequence. These results establish a quantitative connection between Causal-Smoothing theory, relativistic compact stars, and future binary-pulsar tests while identifying realistic-EOS calculations and nonlinear stellar solutions as important next steps.