Introduction to Cosmology

70 Tests of General Relativity

Observer

plane

Strong

lensing

Weak

lensing

DS

DL DLS

θI θS

αg θI*

Lens

plane

Source

plane

Figure 4.1A gravitationally lensing cluster. Wavefronts and light rays are shown. The geometry

is described in the text.

of the source on the sky, respectively. Weak lensing is defined as events where the
potential is weak and the light ray clearly avoids the lensing object (the lower light
ray in Figure 4.1). The field equations of GR can then be linearized.
For the special case of a spherically or circularly symmetric gravitating body such
as the Sun with mass푀inside a radius푏, photons passing at distance푏of closest
approach would be deflected by the angle (Problem 2)

훼=

4 GM

푏푐^2

. (4.4)

For light just grazing the Sun’s limb (푏= 6. 96 × 108 m), the relativistic deflection is

훼= 1. 750 ′′, whereas the nonrelativistic deflection would be precisely half of this.

To observe the deflection one needs stars visible near the Sun, so two conditions

must be fulfilled. The Sun must be fully eclipsed by the Moon to shut out its intense

direct light, and the stars must be very bright to be visible through the solar corona.

Soon after the publication of Einstein’s theory in 1917 it was realized that such a

fortuitous occasion to test the theory would occur on 29 May 1919. The Royal Astro-

nomical Society then sent out two expeditions to the path of the eclipse, one to Sobral

in North Brazil and the other one, which includedArthur S. Eddington(1882–1944),

to the Isle of Principe in the Gulf of Guinea, West Africa.

Both expeditions successfully observed several stars at various distances from the

eclipsed Sun, and the angles of deflection (reduced to the edge of the Sun) were