Relativistic Radiative Hydrodynamic Framework for the Nuclear Impact Hypothesis: Implications for Protostellar Ignition and Planetary Ejection

This manuscript presents a comprehensive relativistic radiative hydrodynamic framework for the Nuclear Impact Hypothesis, which posits that a hypervelocity nuclear aggregate impactor ($v_0 \gtrsim 1500$ km s$^{-1}$) could initiate proto-solar ignition and asymmetrically eject nascent planetary embryos through magnetocentrifugal thrust in a radiation-dominated proto-stellar environment. The framework integrates Poisson's equation for gravitational potentials, special relativistic momentum conservation, Lorentz forces in magnetized plasmas, three-temperature radiation hydrodynamics, and relativistic Rankine-Hugoniot shock relations, rendering it applicable across diverse stellar configurations. High-resolution cubic interpolation of helioseismologically constrained Standard Solar Model (SSM) profiles (deviations $\lesssim 8\%$) yields penetration depths $\delta \approx 0.005 R_\odot$ prior to electromagnetic disassembly and ablation-mediated fragmentation in neutral proto-stellar cores. This is achieved via refined modeling of relativistic drag and disassembly criteria, ensuring robust convergence with observational benchmarks. The ejection mechanism leverages magnetocentrifugal thrust $a_\mathrm{thrust} = \omega^2 r (B^2 / 4\pi \rho) \gtrsim 10^{-3} c^2 / R_\odot$, propelled by proto-stellar rotation and magnetism, facilitating escape from $r_0 = 0.1 R_\odot$ at terminal velocities $v_\infty \sim 45$ km s$^{-1}$, consistent with orbital circularization and radiative equilibration timescales. Variance-based global Sobol sensitivity analysis ($N=2048$) underscores the predominance of initial velocity ($S_{v_0}=0.65$) and thrust ($S_{a_\mathrm{thrust}}=0.58$), with second-order interactions $V_{ij} \approx 0.05$. Bayesian uncertainty propagation delivers $\mu_\delta = 0.005 \pm 0.001 R_\odot$. Falsifiability is anchored in anticipated Gaia DR4 transients and meteoritic isotopic disequilibria. Grounded in solar wind plasma diagnostics \cite{kasper2016sweap} and relativistic merger hydrodynamics \cite{hu2024energetic,chan2024distinct}, the framework forecasts shock-induced thermonuclear ignition ($\dot{E}_\mathrm{diss} \sim 10^{22}$ erg cm$^{-3}$ s$^{-1}$) and density-selective embryo expulsion ($\rho > 10$ g cm$^{-3}$), offering profound insights into Solar System formation and interstellar probe resilience.