Graphical Analysis of Gravitational Time Dilation near a Schwarzschild Black Hole

Time poses an interesting behavior near blackholes.The heavy mass and great density of the black holes slow down even time itself.Gravitational time dilation, a direct prediction of Einstein's general theory of relativity, quantifies how clocks tick slower in stronger gravitational fields.In this paper, the behavior of time near a non-rotating (Schwarzschild) black hole is analyzed using a graphical approach.The time dilation factor is modeled as a function of radial distance from the black hole, with particular emphasis on its behavior near the Schwarzschild radius.By expressing the relation in a generalized, scale-independent form, the dependence of time dilation on radial position alone is examined.A graphical analysis shows that the time dilation factor approaches zero as the radial distance approaches the Schwarzschild radius, indicating extreme slowing of time relative to a distant observer, while approaching unity far from the black hole.The results highlight the non-linear nature of gravitational time dilation and clarify the distinction between proper time experienced near the event horizon and time measured by a distant observer.________________________________________________________________________________________________________