What are super-translations? There's been a lot of news lately about a possible solution to the black hole information paradox from a presentation given by Stephen Hawking to the KTH Royal Institute of Technology in Stockholm. Many of them mention the term super translation.
This article, for example, states (with emphasis added):

His flash of inspiration came when listening to a lecture in April
  about what are called super-translations, a bit of the heady
  branch of mathematics known as group theory. Dr Hawking thinks that
  incoming particles shed their information like a coat as they pass
  into a black hole, leaving it draped on the event horizon itself.
  Super-translations mathematically describe how that information influx can slightly jiggle the fabric of space at the horizon, in turn
  shifting around when and how the black hole radiates.

What exactly are super-translations, mathematically?
I have been trying to search for this term online, but the results are flooded with news articles. Where can I find some sources that describe super-translations in greater detail?
EDIT: Another description of super-translations is provided in a recent article:

The horizon of a black hole has the weird feature that it’s a sphere
  and it’s expanding outward at the speed of light. For every point on
  the sphere, there’s a light ray. So it’s composed of light rays. But
  it doesn’t get any bigger and that’s because of the force of gravity
  and the curvature of space. And, by the way, that’s why nothing that
  is inside a black hole can get out—because the boundary of the black
  hole itself is already moving at the speed of light.
There’s this symmetry of a black hole that we all knew about in which
  you move uniformly forward and backward in time along all of the light
  rays. But there’s another symmetry, which is the new thing in this
  paper (though various forms of it have been discussed elsewhere). It’s
  a symmetry in which the individual light rays are moved up and down.
  See, individual light rays can’t talk to each other—if you’re riding
  on a light ray, causality prevents you from talking to somebody riding
  on an adjacent light ray. So these light rays are not tethered
  together. You can slide them up and down relative to one another. That
  sliding is called a super-translation.
And in a way, it looks like you're not doing anything. Think of a
  bundle of infinitely long straws and you move one up and down relative
  to the other. Are you doing anything, or not? What we showed is that
  you are doing something. It turns out that adding a soft graviton has
  an alternate description as a super-translation in which you move some
  of these light rays back and forth relative to one another.
That’s super-translations on black holes. Super-translations were
  introduced in the 1960s, and they were talking not about the light
  rays that comprise the boundary of spacetime at the horizon of a black
  hole but the light rays that comprise the boundary of spacetime out at
  infinity. The story started by analyzing those supertranslations.

 A: A suprertranslation is a diffeomorphism on an asymptotically-flat Riemannian or pseudo-Riemannian manifold, such that the result is also asymptotically-flat. (The diffeomorphism doesn't need to be an isometry).
(Of course, I didn't define asymptotic-flattness. I don't know the definition, but do know that in an asymptotically-flat manifold if you go far-enough in any direction, the metric becomes close to being flat as you wish).
The group of suprertranslations of a certain manifold is called the BMS group, after Bondi,Van der Burg and Sachs who discussed them in the context of gravitational waves in the following papers:
*Bondi, Hermann, M. G. J. Van der Burg, and A. W. K. Metzner. "Gravitational waves in general relativity. VII. Waves from axi-symmetric isolated systems." Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. Vol. 269. No. 1336. The Royal Society, 1962.
*Sachs, Rainer K. "Gravitational waves in general relativity. VIII. Waves in asymptotically flat space-time." Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. Vol. 270. No. 1340. The Royal Society, 1962.
