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Volume 35: Pages 25-26, 2022
Coordinates in general relativity: Frequency shift
Wenbin Lin1,2,a)
1School of Mathematics and Physics, University of South China, 28 Changsheng West Road, Hengyang 421001, China;
2School of Physical Science and Technology, Southwest Jiaotong University, 111 North 1st Section, Second Ring Road, Chengdu 610031, China;
It is easily shown that the theoretical calculations for the frequency shift in the Schwarzschild spacetime under the standard, isotropic, and harmonic coordinates are different. Since the relations between these coordinates and the observer’s reference frame are not clear, it remains an unsolved problem to make the coordinate-independent prediction for the frequency shift when the light comes from the extremely strong gravitational fields, for example, the light emitter is near to the horizon of black holes or the surface of neutron stars.
On montre facilement que les calculs théoriques pour le déplacement de fréquence dans l'espace-temps de Schwarzschild sous les coordonnées standard, isotropes et harmoniques sont différents. Étant donné que les relations entre ces coordonnées et le cadre de référence de l'observateur ne sont pas claires, il reste un problème non résolu de faire la prédiction de la coordonnée indépendante pour le déplacement de fréquence lorsque la lumière provient des champs gravitationnels extrêmement forts, par exemple, l'émetteur de lumière est proche à l'horizon des trous noirs ou à la surface des étoiles à neutrons.
Key words: Coordinates; General Covariance; Frequency Shift; Schwarzschild Spacetime.
Received: September 26, 2021; Accepted: December 24, 2021; Published Online: January 25, 2021
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