What effect shifts light to longer wavelengths as it escapes a black hole's gravity?

The effect that shifts light to longer wavelengths as it escapes a black hole’s gravity is gravitational redshift.

A photon climbing out of a gravitational well is measured by a distant observer with lower frequency and longer wavelength than when it was emitted. In general relativity, this follows from the different rates at which clocks run at different gravitational potentials. The effect becomes increasingly strong as the emission point approaches a black hole’s event horizon.

Gravitational redshift is not the same as an ordinary Doppler shift, although motion of the source or observer can produce an additional Doppler component. It is also the reverse of gravitational blueshift, which occurs when light moves downward into a gravitational well. For a Schwarzschild black hole, light emitted exactly at the event horizon cannot reach a distant observer, so the idealized redshift grows without bound as the horizon is approached from outside.

Einstein predicted the effect in 1907, and the Pound–Rebka experiment confirmed gravitational frequency shifts on Earth in 1959.