Schwarzschild Geodesics - Bending of Light By Gravity

Bending of Light By Gravity

See also: Gravitational lens and Shapiro delay

In the limit as the particle mass m goes to zero (or, equivalently, as the length-scale a goes to infinity), the equation for the orbit becomes

$\varphi = \int \frac{dr}{r^{2} \sqrt{\frac{1}{b^{2}} - \left( 1 - \frac{r_{s}}{r} \right) \frac{1}{r^{2}}}}$

Expanding in powers of r_s/r, the leading order term in this formula gives the approximate angular deflection δφ for a massless particle coming in from infinity and going back out to infinity:

$\delta \varphi \approx \frac{2r_{s}}{b} = \frac{4GM}{c^{2}b}.$

Here, b can be interpreted as the distance of closest approach. Although this formula is approximate, it is accurate for most measurements of gravitational lensing, due to the smallness of the ratio r_s/r. For light grazing the surface of the sun, the approximate angular deflection is roughly 1.75 arcseconds, roughly one millionth part of a circle.

Read more about this topic: Schwarzschild Geodesics

Famous quotes containing the words bending, light and/or gravity:

“Back from that great-grandfather I have come
to puzzle a bending gravestone for his sake,
to question this diminishing and feed a minimum
of children their careful slice of suburban cake.”
—Anne Sexton (1928–1974)

“Its quick silver bell beating, beating
And down the dark one ruby flare
Pulsing out red light like an artery,”
—Karl Shapiro (b. 1913)

“Here I sit down to form characters. One I intend to be all goodness; All goodness he is. Another I intend to be all gravity; All gravity he is. Another Lady Gish; All Lady Gish she is. I am all the while absorbed in the character. It is not fair to say—I, identically I, am anywhere, while I keep within the character.”
—Samuel Richardson (1689–1761)