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Galaxies at the far limit of the visible universe are moving away from us near the speed of light. There may be some beyond that that are moving away from us faster, so the universe appears to have an event horizon beyond which stuff is moving away from us so fast that we cannot see it.

There is another event horizon called a Rindler horizon, that arises when anything is accelerated. There will be a region of space-time that is left behind by the acceleration and consequently has no chance of ever catching up - resulting in a dynamic event horizon. You'd need a big acceleration for it to measurable.

It has postulated that electrons being accelerated around a gold nano tip do indeed reveal this event horizon because of the observed Unruh radiation.

But if the electrons in that experiment are being accelerated around the tip, that is, not a linear acceleration, can that still cause a Rindler horizon?

So why don't the stars disappear when I spin around, since by doing so I made them travel faster than light?

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The Rindler geometry is time independent, that is it describes the spacetime geometry for an observer who has always been accelerating at a constant value and will always accelerate at a constant value. The existence of the Rindler horizons (there is a white hole horizon as well) depend on this time independence. For a real observer who started accelerating only a finite time ago and will stop accelerating at some finite time in the future only apparent horizons exist. So you do not create the Rindler horizons the moment you start accelerating.

You might be interested to read this answer to What is the proper way to explain the twin paradox?. This explains how an inertial observer sees no horizon while the Rindler observer does see a horizon. Understanding the Rindler horizon is a good way to understand other coordinate singularities like the event horizon of a black hole.

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  • $\begingroup$ Does that mean black holes have to have always existed so that they have a constant and always existing gravitational acceleration, in order to have an event horizon? $\endgroup$ Commented Jul 28, 2016 at 16:04
  • $\begingroup$ @user2800708: the analytic black hole solutions, the Schwarzschild, Reissner-Nordstrom, Kerr and Kerr-Newman geometries, are all time independent just like the Rindler geometry. Any real black hole will have only an apparent horizon. See this answer of mine for more on this. $\endgroup$ Commented Jul 28, 2016 at 16:06
  • $\begingroup$ What about the gold nano tip experiment, do you think it really exhibits an apparent horizon and observable Unruh radiation? $\endgroup$ Commented Jul 28, 2016 at 16:09

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