Derivation of gravitational time dilation from principle of equivalence and special relativity

Abstract

General relativity is the exact theory of gravity which has been experimentally found to be correct with extremely high accuracy. One of the most surprising predictions of the general theory is that time runs slow in a gravitational field. Its proof formally comes from Schwarzschild metric which is a solution of Einstein field equation for a spherically symmetric mass. However, as Einstein field equation is too complex, attempts have been made earlier to derive gravitational time dilation by direct use of principle of equivalence and special theory of relativity. But, this objective has been accomplished partially till date as the resulting expression agrees with the exact expression only upto first order. In this paper, by using principle of equivalence and special relativity, we present a thought experiment which helps us to derive an expression that exactly matches with the expression for gravitational time delay.