Recharacterizing Dark Matter Effects Through Inertial Principles in General Relativity

The observational evidence for dark matter presents one of the most significant challenges in modern physics. This paper proposes a novel theoretical framework that reinterprets the gravitational effects traditionally attributed to dark matter as manifestations of modified inertial principles within General Relativity. By reconceptualizing inertia at galactic scales and leveraging the equivalence principle, this approach eliminates the need for exotic dark matter particles while maintaining consistency with astronomical observations. The framework demonstrates how purely geometrical aspects of spacetime, when fully considered, can account for galactic rotation curves and other phenomena currently attributed to dark matter, potentially resolving a major cosmological mystery through mathematical principles rather than new particles.