Twin paradox in curved spacetime

Abstract

The twin paradox has played an important role in the history of special relativity (SR). A precise calculation would require the application of the general theory of relativity (GR) but, neglecting the acceleration phases of the traveling twin, even in SR it is possible to find the correct solution without logical contradictions. Nowadays it is well known that the twin thought experiment seems a paradox as a consequence of a naive application of time dilation and the principle of relativity. The twin who goes on space travel is the one who, returning to the twin at rest, finds the aged brother. Continuing in this pedagogical tradition, we want to add a further consideration. In fact, the experiment has always been explained by considering the two twins immersed in Minkowski’s spacetime. It could be interesting, from a didactic point of view, to analyze the same thought experiment without neglecting the Earth’s gravitational field. Indeed, under certain conditions, it may happen that the traveling brother can grow older than his brother at rest