Editing Gravitational lens (section)

==Explanation in terms of spacetime curvature==
{{See also|Kepler problem in general relativity}}
[[Image:Black hole lensing web.gif|thumb|Simulated gravitational lensing (black hole passing in front of a background galaxy)]]
In general relativity, light follows the curvature of spacetime, hence when light passes around a massive object, it is bent. This means that the light from an object on the other side will be bent towards an observer's eye, just like an ordinary lens. In general relativity the path of light depends on the shape of space (i.e. the metric). The gravitational attraction can be viewed as the motion of undisturbed objects in a background curved ''[[geometry]]'' or alternatively as the response of objects to a ''force'' in a flat geometry. The angle of deflection is

: <math>\theta = \frac{4GM}{c^2 r}</math>

toward the mass ''M'' at a distance ''r'' from the affected radiation, where ''G'' is the [[Gravitational constant|universal constant of gravitation]], and ''c'' is the speed of light in vacuum.

Since the [[Schwarzschild radius]] <math>r_\text{s}</math> is defined as <math>r_\text{s} = 2Gm/c^2</math>, and [[escape velocity]] <math>v_\text{e}</math> is defined as <math display="inline">v_\text{e} = \sqrt{2Gm/r} = \beta_\text{e} c</math>, this can also be expressed in simple form as

: <math>\theta = 2 \frac{r_\text{s}}{r} = 2 \left(\frac{v_\text{e}}{c}\right)^2 = 2\beta_\text{e}^2.</math>