Relativistic tidal forces.

Details Relativistic tidal forces. Relativistic tidal forces.

Oct 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999hadj...22..547m&link_type=abstract

Hadronic J., Vol. 22, No. 5, p. 547 - 562

Computer Science

Relativity Theory: Tidal Effects

Scientific paper

Einstein's general relativity is a relativistic theory of gravity, which assumes an invariance of the (bending) light path under a generalized Galileo-Lorentz transformation. The first term in the nonrelativistic limit of the Einstein equation of motion is the Newtonian equation of motion under the Newtonian gravitational force, but Einstein's theory gives additional terms, particularly terms that depend on the velocities of a test particle and gravitational sources, and they are the relativistic correction terms. Because of Galileo's equivalence principle, we, staying on Earth, can observe only tidal components of gravitational forces due to the Sun, the moon, and the galactic center. The tidal components are obtained by Synge as geodesic deviations in general relativity. Instead of approaching the problem using a geodesic deviation, it is easier to linearize Einstein's theory first, obtaining the relativistic correction terms to the Newtonian gravitational force, and then obtain relativistic corrections to the tidal force. In the linearized theory one can take into account more than two sources by simply adding them. The author examines the tidal forces systematically.

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