Radial Dependence of Gravitational Time Dilation: A Comparative Boundary Analysis of Stellar Remnants

When massive stars reach the end of their lifecycles, they leave behind dense remnants characterised by intense gravitational pull.This study examines the boundaries of gravitational time dilation surrounding these theoretical stellar cores.By applying the exterior Schwarzschild metric, we express time dilation solely as a function of radial distance from the center of mass.This approach yields an analytical and graphical demonstration of the unique spatial properties that differentiate neutron stars from black holes.Specifically, we show that the time dilation curve for a neutron star abruptly ends at its physical surface, determined by the nuclear equation of state, while the curve for a black hole extends indefinitely, approaching the event horizon where a distant observer would perceive time as coming to a standstill.AI has been used for the better framing of content.