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Summary

Parallel transport of vectors and tensor densities along curves is defined using the covariant derivative. A geodesic is defined as such a curve, along which the tangent vector, when parallely transported, is collinear with the tangent vector defined at the endpoint. Affine parametrisation is introduced.

Summary

We calculate “deflection of light by the Sun." First, we define a first-order action for a massless particle moving in a gravitational field, and then we calculate the motion of light on a geodesic as motion of light in a medium with a small, position-dependent index of refraction, giving the light deviation for small angles. Then we redo the calculation from the Hamilton–Jacobi formalism by first defining the Hamilton–Jacobi equation for light motion and then solving it. This gives the nonperturbative light deviation that matches the previous calculation at small angles. We end by comparison with the deflection of light by the Sun in special relativity, which is different by a factor of 2.

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5 - Parallel transport and geodesic lines

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42 - Deflection of Light by the Sun and Comparison with General Relativity

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2 results

5 - Parallel transport and geodesic lines

Summary

42 - Deflection of Light by the Sun and Comparison with General Relativity

Summary