How close can an observer approach the black hole in an unpowered flyby without falling into it?

In classical mechanics by choosing the right trajectory you can approach a planet arbitrarily closely, if there is no atmosphere or anything to slow you down, you can approach the surface then fly away without firing your rockets.

Does the same works in general relativity with black holes? Can you do close approach of the event horizon without falling in?

(My guess is that it's the distance of the photon sphere, but it's just a guess.)

To be more specific:

• observer much smaller than the black hole, so you can assume it's a point particle. And won't be torn apart by tidal forces above the horizon.
• Assume a flyby: The observer must be able to escape to the infinity unpowered.
• Assume the black hole doesn't have accretion disk.
• I don't mind if it's rotating, but if it's simpler to make calculations in terms of a non-rotating black hole I accept it too.
• As long as you don't fall into the event horizon... – TanMath Dec 7 '14 at 0:20
• Do you mean hypothetically (i.e. a point-particle approaching a black hole with nothing else around), or realistically (i.e. a big spaceship approaching a rotating black hole with an accretion disc etc)? – jabirali Dec 7 '14 at 0:48