[Harri (OP)]

Rather than with the obvious use of mirrors, is it possible for light to double back on itself in outer space? I see the way large mass objects warp time and space and affect the route light takes from distance stars. Is it possible that something like a black hole could act as a roundabout and send light back in the same direction it came?  Or perhaps in the case of a black hole anything like a turnaround would result in the light getting swallowed up?

[evan_au]

Yes.

The Sun can bend light by a tiny angle - something like one thousandth of a degree.

But a black hole can bend light by any arbitrary angle:
- 90° left turn
- 180° U-Turn
- 270° right turn
- 360° continue on in the original direction
- In fact, there are regions around the black hole where light will take 2, 3, 4 or more orbits around the black hole before escaping.

But most light rays approaching a black hole will end up being swallowed inside the event horizon.

[Halc]

Evan's answer is spot on.  In Newtonian physics, objects would always take a hyperbolic path around an object that it isn't orbiting, which leads to a return path up to but not including 180°, but under GR, there's no limit to the bending.
There is a photo-sphere for a Schwarzschild black hole which is 1.5 the distance from the event horizon. If light reaches that radius, there is no path for it to escape without use of something like mirrors. The closer it gets to that radius, the more it bends, which leads to the scenario described above with the multiple laps before escape.

[Malamute Lover]

Evan's answer is spot on.  In Newtonian physics, objects would always take a hyperbolic path around an object that it isn't orbiting, which leads to a return path up to but not including 180°, but under GR, there's no limit to the bending.
There is a photo-sphere for a Schwarzschild black hole which is 1.5 the distance from the event horizon. If light reaches that radius, there is no path for it to escape without use of something like mirrors. The closer it gets to that radius, the more it bends, which leads to the scenario described above with the multiple laps before escape.

The photosphere for a Schwarzschild (non-rotating) black hole is half the black hole radius above the event horizon, not 1.5 times. This is the lowest height above the event horizon where photons can orbit.

The radius of a Schwarzschild black hole is equal to the radius of a hypothetical Euclidean sphere having the same circumference as the black hole. (The distance from the event horizon to the hypothetical singularity inside the black hole is not easily defined.) The formal definition for black hole radius is somewhat different from my geometric analog but amounts to the same thing for a Schwarzschild black hole. The formal definition allows defining the radius for Kerr (rotating) black holes, which are not simple shapes.

A photon that crosses the photosphere from outside cannot escape except as you say with mirrors. There is too much ‘down’ in the spacetime geometry. However, a photon originating within the photosphere can escape if it is pointed sufficiently upward.  How much ‘up’ is sufficient depends on how high above the event horizon it originates (or is reflected). Even a photon originating from very near the event horizon can still escape if it is pointed directly up or nearly so. The escape velocity does not reach c until the event horizon itself. However, because of time dilation in the neighborhood of a black hole, it could take a long time to get free of the region. The deeper down it starts, the longer it will take.


EDIT: The first item in the Similar Topics list concerns seeing the past by reflection from a mirror at a great distance. I am reminded of the old 1930s movie The Invisible Ray where this is somehow accomplished and the earth of millions of years ago is observed in a telescope.

[Halc]

There is a photo-sphere for a Schwarzschild black hole which is 1.5 the distance from the event horizon.

The photosphere for a Schwarzschild (non-rotating) black hole is half the black hole radius above the event horizon, not 1.5 times.

Poorly worded on my part perhaps, trying to say 1.5 times the radius of the event horizon, not 1.5 that radius from said horizon. But I used 'from', which could convey a different meaning.