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Physics and Astronomy (1)

schwarzschild metrix

Cambridge University Press (1)

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3 - Geodesics
Brian P. Dolan, National University of Ireland, Maynooth
Book:

Einstein's General Theory of Relativity

Published online:

15 June 2023

Print publication:

29 June 2023, pp 44-84
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Summary

Geodesics are introduced and the geodesic equation analysed for the geometries introduced in chapter 2, using variation principles of classical mechanics. Geodesic motino on a sphere is described as well as the Coriolis effect and the Sagnac effect. Newtonian gravity is derived as the non-relativistic limit of geodesic motion in space-time. Geodesics in an expanding universe and heat death is described. Geodesics in Schwarzschild space-time are treated in detail: the precession of the perihelion of Mercury; the bending of light by the Sun; Shapiro time delay; black holes and the event horizon. Gravitational waves and gravitational lensing are also covered.