Geometric Interpretation of Inertial Divergence and Time Dilation in Schwarzschild Spacetime via 5D Null Trajectories

This paper presents a geometric interpretation of the divergent proper acceleration and gravitational redshift experienced by a static observer near a Schwarzschild event horizon. Operating within a 5D null framework (ds52=0ds52=0), we do not introduce quantitative corrections to General Relativity; rather, we propose that inertia emerges dynamically as the geometric cost of reorienting a 5D null trajectory. We demonstrate that the infinite proper acceleration required to maintain a static position at r→rsr→rs is not merely a coordinate artifact, but a strict kinematic boundary: the “Null Phase Space Saturation.” By explicitly evaluating the differential relationship and defining a rigorous geometric rigidity operator R≡∣dvχ/dv4∣=(v4/c)γ(v4)R≡∣dvχ/dv4∣=(v4/c)γ(v4), we show that as the 4D spatial velocity of the static observer relative to a local inertial frame approaches cc, the extra-dimensional velocity component vχvχ vanishes, causing the resistance to reorientation to diverge. We contrast this with a free-falling observer, for whom this 5D kinematic saturation is non-existent. Finally, we provide a unified geometric perspective where 4D proper time, gravitational redshift, and the halting of extra-dimensional flow are strictly equivalent.