Lorentz covariant theory of light propagation in gravitational fields of arbitrary-moving bodies

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 60, Issue 12, 1999, Pages

  Kopeikin, Sergei M ^a   Schäfer, Gerhard ^a  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

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[No Author keywords available]

Indexed keywords

EID: 17044383388     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.60.124002     Document Type: Article

References (156)

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13. In what follows we shall often use geometrical units, e.g., see Ref. 5 in which (Formula presented)
14. The difference between the parameters (Formula presented) and (Formula presented) includes terms of the post-Newtonian order of magnitude. In the weak-field limit the numerical value of (Formula presented) coincides with that of (Formula presented) which is one of the parameters of the standard parametrized post-Newtonian (PPN) formalism 9. For more details see Refs. 1415, and references therein.
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65. Synge calls the relationship (78) the Doppler effect in terms of frequency (see Ref. 62, p. 122). It is fully consistent with definition of the Doppler shift in terms of energy (see Ref. 62, p. 231) when one compares the energy of photon at the points of emission and observation of light. The Doppler shift in terms of energy is given by (Formula presented)where (Formula presented) (Formula presented) and (Formula presented) (Formula presented) are the four-velocities of source of light and observer and the four-momenta of photon at the points of emission and observation respectively. It is quite easy to see that both mentioned formulations of the Doppler shift effect are equivalent. Indeed, taking into account that (Formula presented) and (Formula presented), where (Formula presented) is the phase of the electromagnetic wave, we obtain (Formula presented) Thus, (Formula presented)The phase of electromagnetic wave remains constant along the light ray trajectory. For this reason, (Formula presented), and Eq. (78) holds.
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