So it's possible for a beam of light to wrap around a black hole and intersect its own path. This must mean that light doesn't follow Kepler orbits[1] in general relativity?
> This must mean that light doesn't follow Kepler orbits[1] in general relativity?
That's right. This is true even in the weak field limit: the orbits of planets in the Solar System are not exact ellipses when GR is taken into account. This is called "perihelion precession", and was observed with Mercury even in the 19th century; it was one of the "classic tests" that Einstein calculated to satisfy himself that GR was correct. With modern observations I believe this effect has been observed for at least all of the inner planets (Mercury, Venus, Earth, and Mars).
I see, so GR causes all orbits to precess, and actually nothing follows classical Kepler orbits exactly. Even the simple two-body problem doesn't result in elliptical orbits.
Yes. (Strictly speaking, a perfectly circular orbit would qualify as a "classical Kepler orbit", and is still possible in GR, but this is an idealized case.)
[1] i.e. ellipse, parabola, or hyperbola: http://en.wikipedia.org/wiki/Kepler_orbit