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