Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-10-16
Class.Quant.Grav. 19 (2002) 571-578
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Revtex, 5 p. Rewritten Sec. II, minor changes in Secs III - VII. To appear in the Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/19/3/311
The gravitational redshift formula is usually derived in the geometric optics approximation. In this note we consider an exact formulation of the problem in the Schwarzschild space-time, with the intention to clarify 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 the backscattering can lead to significant modifications. The obtained results 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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