Revisiting the Event Horizon: A Classical and Relativistic Reassessment of the Schwarzschild Radius

The Schwarzschild radius is conventionally interpreted as the event horizon of a
Schwarzschild black hole, based on the condition that the escape velocity equals the
speed of light. In this work, we identify two fundamental inconsistencies in this interpretation.
First, a classical analysis of tangential escape velocity—derived from
the balance between centrifugal and gravitational forces—indicates that the velocity
reaches the speed of light at half the Schwarzschild radius. This challenges the conventional
definition of the event horizon. Second, within a relativistic framework, the
kinetic energy of a particle diverges as its speed approaches that of light, implying that
the escape velocity at the Schwarzschild radius is strictly less than the speed of light.
These observations collectively suggest that the Schwarzschild radius cannot serve as
a true boundary for black holes in either classical or relativistic regimes. To address
this issue, we propose a modified form of the Schwarzschild metric that eliminates
the coordinate singularity, aligns with relativistic energy considerations, and remains
consistent with the weak-field limit of general relativity.