A Relativistic Radiative Hydrodynamic Framework for the Nuclear Impact Hypothesis: Implications for Proto-Stellar Ignition and Planetary Ejection

This manuscript delineates a relativistic radiative hydrodynamic framework underpinning the Nuclear Impact Hypothesis, which posits that a hypervelocity nuclear impactor (v₀ ≳ 10³ km s⁻¹) could precipitate proto-solar ignition and the ejection of nascent planetary embryos through asymmetric magnetocentrifugal thrust in a radiation-dominated proto-stellar milieu. The formulation integrates Poisson's equation for gravitational potentials, special relativistic momentum conservation, augmented Lorentz forces in magnetized plasmas, three-temperature radiation hydrodynamics, and relativistic Rankine-Hugoniot shock relations, extensible to heterogeneous stellar configurations. High-resolution simulations, leveraging cubic interpolation of helioseismically constrained Standard Solar Model profiles (deviations ≲ 8%), delineate penetration depths δ ≲ 0.05 R_⊙ antecedent to electromagnetic disassembly and ablation-mediated fragmentation within neutral proto-stellar cores. The posited ejection paradigm, actuated by magnetocentrifugal thrust a_thrust = ω² r (B² / 4π ρ) ≳ 10⁻³ c² / R_⊙ from proto-stellar rotation and magnetism, engenders egress from r₀ = 0.1 R_⊙ at asymptotic velocities v_∞ ∼ 40 km s⁻¹, consonant with orbital circularization and radiative equilibration timescales in archetypal systems. Variance-based global Sobol sensitivity analysis (N=2048) underscores the preeminence of initial velocity (S_{v₀}=0.65) and thrust (S_{a_thrust}=0.58), corroborated by Bayesian propagation affording μ_δ = 0.048 ± 0.012 R_⊙. Falsifiability anchors to anticipated Gaia DR4 transients and meteoritic isotopic disequilibria. Anchored in solar wind plasma diagnostics [kasper2016sweap] and relativistic merger hydrodynamics [hu2024energetic,lee2025aic], this rigorous construct hypothesizes shock-fostered thermonuclear ignition (Ė_diss ∼ 10²² erg cm⁻³ s⁻¹) and density-discriminatory embryo expulsion (ρ > 10 g cm⁻³), proffering mechanistic insights into Solar System ontogeny and resilience paradigms for interstellar instrumentation.