gravitational redshift

Light climbing out of a gravity well loses energy on the way up, and since a photon's energy is tied to its frequency, its color shifts toward the red. Equivalently, and more strikingly, clocks deeper in a gravitational field run slow: a clock at sea level ticks measurably slower than an identical clock on a mountaintop. This is gravitational redshift, and it is one of the simplest and most directly tested consequences of curved spacetime.

For a weak field the fractional shift is Delta f / f = -Delta phi / c^2, or Delta f / f = -g h / c^2 for a height h in gravity g, so raising a clock by one meter on Earth speeds it up by about one part in 10^16. The full, strong-field result comes straight from the Schwarzschild metric: a signal sent from radius r_emit to a faraway receiver is redshifted by the factor f_received / f_emitted = sqrt(1 - r_s / r_emit), which drops to zero right at the horizon, where light is redshifted without limit. The effect is really about the metric's time-time component g_tt slowing the flow of proper time deeper in the well.

You meet gravitational redshift every time you use satellite navigation: the atomic clocks aboard GPS satellites, higher in Earth's field, run fast relative to ground clocks by tens of microseconds per day, and the system must correct for it or positions would drift by kilometers. A worthwhile honesty: the leading effect follows from the equivalence principle and energy conservation alone, without the full machinery of general relativity, which is why it was one of the earliest predictions and why Pound and Rebka could confirm it in 1959 with photons rising just 22.5 meters up a Harvard tower.