In a static spacetime with , a photon has conserved Killing energy . A static observer with four-velocity measures frequency proportional to . Hence light emitted at one lapse and received at another obeys the displayed ratio. For it gives the weak-field shift . This local clock effect does not require light-ray bending.
An upward photon has lower received frequency when compared with the receiver's local clock: makes the shift negative. The corresponding upper clock runs faster in a comparison using the same static time coordinate. These are reciprocal descriptions of gravitational redshift and gravitational time dilation, not opposite predictions. A locally measured speed of light remains .
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Gravitational redshift is a phenomenon predicted by Einstein's theory of general relativity, which describes how light is affected by the presence of a gravitational field. It refers to the shift of light (or other electromagnetic radiation) to longer wavelengths as it escapes from a massive object, such as a star or a black hole. Here's how it works: when light is emitted from the surface of a massive body, it climbs out of the gravitational well created by that mass.