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Recently we made the very first real photo of a BH.

Now there are other questions on this site about BH length contraction, none of them answers my question.

Do black holes exhibit length contraction just like anything else being observed moving at high velocity?

Now as I understand, if a BH is moving relative to us, observers at relativistic speeds, a phenomenon called Terrell rotation will appear to be visible. This is due to SR length contraction.

On the picture the accretion disk is what we see mostly, might seem to us to undergo this rotation effect.

Terrell rotation or Terrell effect is the visual distortion that a passing object would appear to undergo, according to the special theory of relativity if it were travelling a significant fraction of the speed of light.

https://en.wikipedia.org/wiki/Terrell_rotation

enter image description here

Is this image I modified somewhat correct?

Question:

  1. Should a relativistic BH's (moving relative to us) undergo length contraction (Terrell rotation)?
Árpád Szendrei
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1 Answers1

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We can answer this using just special relativity, if we restrict to observers far from the black hole. In fact the source of light does not matter. Here is why.

Take two observers, both far from the source (be it stuff in orbit around a black hole, or whatever). One observer moves rapidly relative to the other, along the direction at right angles to the direction to the source. The light arriving at both observers is some given set of light waves in the given region of spacetime, and that region is far from any gravitating source so has no curvature, to very good approximation. Then special relativity tells us all we need to know about the way the two observers see different distributions of light arriving at them at any instant (i.e. on a spacetime plane of simultaneity in their own reference frame). The observations are therefore related by the effect asked about (associated with the name of Terrell) but I don't consider this to be a very important effect. It is just an modest observation about visual appearances.

Andrew Steane
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