Authors: John Hogarth
Schwarzschild’s gravitational time dilation expression is derived assuming a ~flat Minkowski spacetime. This time dilation effect is spherically symmetric, occurring in all radial directions for a gravitational source. A way to derive Schwarzschild’s expression is with a model that assumes a mass starting from rest at some distance from a gravitational field source (such as Earth). One can use Newtonian Kinetic Energy and Gravitational Potential Energy to create an energy balance. This is then used to derive escape velocity: the mass steadily starts moving through the gravitational potential field, gaining speed until it hits escape velocity upon reaching the gravitational field source. This document explores the derivation using escape velocity. Moreover, this document modifies the approach by using relativistic mass to derive a slightly different expression for gravitational time dilation. Finally, alternative interpretation of gravitational time dilation is also explored, using the concept of relativistic mass.
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