Abstract
The gravitational redshift formula is usually derived in the geometric optics approximation. In this paper we consider an exact formulation of the problem in the Schwarzschild spacetime, with the intention of clarifying under what conditions this redshift law is valid. It is shown that in the case of shocks, the radial component of the Poynting vector can scale according to the redshift formula, under a suitable condition. If that condition is not satisfied, then the effect of backscattering can lead to significant modifications. The results obtained imply that the energy flux of the short wavelength radiation obeys the standard gravitational redshift formula while the energy flux of long waves can scale differently, with redshifts being dependent on the frequency.
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