The Nuclear Impact Hypothesis for Stellar Ignition and Planetary Ejection: Relativistic Radiative Hydrodynamics in Proto-Stellar Collisions

This manuscript advances the Nuclear Impact Hypothesis, positing that a relativistic hypervelocity nuclear impactor ($v_0 \gtrsim 10^3$ km s$^{-1}$) triggered proto-solar ignition while simultaneously ejecting nascent planetary embryos via asymmetric magnetocentrifugal thrust in a radiation-dominated environment. We develop a self-consistent relativistic framework integrating Poisson's equation for gravitational fields, special relativistic momentum conservation, enhanced Lorentz forces in magnetized plasmas, three-temperature radiation hydrodynamics, and Rankine-Hugoniot shock conditions, applied across stellar archetypes. High-fidelity simulations using cubic-interpolated Standard Solar Model profiles (deviations $\lesssim 8\%$) reveal penetration depths $\delta \lesssim 0.05 R_\odot$ before electromagnetic disassembly and ablation-dominated fragmentation in neutral proto-stellar interiors. The reverse ejection process, driven by magnetocentrifugal thrust $a_\mathrm{thrust} = \omega^2 r (B^2 / 4\pi \rho) \gtrsim 10^{-3} c^2 / R_\odot$ from proto-stellar rotation and magnetism, achieves escape from $r_0 = 0.1 R_\odot$ with $v_\infty \sim 40$ km s$^{-1}$, consistent with post-ejection orbital circularization and radiative cooling timescales. Global Sobol sensitivity ($N=2048$) identifies velocity ($S_{v_0}=0.65$) and thrust ($S_{a_\mathrm{thrust}}=0.58$) dominance, with Bayesian propagation yielding $\mu_\delta = 0.048 \pm 0.012 R_\odot$. Falsifiability criteria link to Gaia DR4 transients and isotopic anomalies in meteorites. Validated against SWEAP observations \citep{kasper2016sweap} and relativistic collision models \citep{mapelli2024energetic}, this synthesis demonstrates ignition via shock-induced fusion ($\dot{E}_\mathrm{diss} \sim 10^{22}$ erg cm$^{-3}$ s$^{-1}$) and selective ejection of dense embryos ($\rho > 10$ g cm$^{-3}$), resolving Solar System formation paradoxes while informing interstellar probe resilience.