I spent some time to study general relativity recently and I found something that confuse me. According to my unserstanding about general relativity, the coordinate velocity of light should be (1-2GM/c(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}r)c, while the wavelength should be (1-2GM/c^{2}r)^{1/2}times its wavelength at infinity, for a photon falling from infinity to the surface of a non-rotating star with radius r with an observer kept stationary on the surface, therefore I conclude that its frequency should be (1-2GM/c^{2}r)^{1/2}times its frequency at infinity, that is , its frequency should be decreased. However I found a textbook , that I do not fully trusted, on general relativity in introductory level said that the frequency should be (1-2GM/c^{2}r)^{-1/2}times its frequency at infinity. That is , the frequency increases. Should the frequency increase or decrease? If I am wrong, please give me a detailed explanation. Thank you.

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# Frequency change of a photon falling to earth

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