/sci/ - Science & Math

This is in the Schwarzschild metric. I just want to be sure about something, the time it would take the light signal to travel from [math] r_1 [/math] to [math] r_2 [/math] and the time it would take from [math] r_2 [/math] to [math] r_1 [/math] is the same, right?

A small part of me says 'no' because the photon would have to fight against the gravitational force when travelling from [math] r_1 [/math] and [math] r_2 [/math], but another part of me says this is nonsensical since photons always travel at the speed of light, the geodesic isn't changing, it shouldn't take a longer time.