[Kryptid (OP)]

If a black hole was travelling at relativistic velocity, would the black hole's event horizon undergo Lorentz contraction? Would such a black hole look like a squashed spheroid instead of a sphere? The event horizon isn't made of matter, which is why I ask.

[LeeE]

Nice question:)

I'm inclined to say yes but I can't formulate a good arguement to support it.

[graham.d]

As stated in another recent post, spheres moving at significant speeds actually "appear" rotated but still spherical. This is a combination of Lorentz contraction and the finite speed of light. (I wish I could find the reference to the erudite paper that presented this surprising fact). I am not sure whether the same would be true of the EH of a BH as light would not be emanating or being reflected from this surface. I think answering this (as with many such questions about physics involving general relativity) are very difficult to answer and could take a long time to calculate by someone with the mathematical knowledge and ability to do so. It doesn't stop the rest of us speculating though :-), but we should treat any answers with scepticism unless backed up with the maths. You can't really just guess...

...but, my guess is that it is affected by Lorentz contraction so would still appear spherical as does any sphere :-)

[graham.d]

This is a good site that has computer simulations

http://www.spacetimetravel.org/

more specifically...

I have not found the original paper on what relativistic objects look like, but here is a more recent one...

http://www.spacetimetravel.org/fussball/fussball.html

[Kryptid (OP)]

How does what a relativistic sphere "appears" to look like correspond to its actual shape? Are they the same or not?

[graham.d]

What a relativistic sphere looks like is how it would look if you took a picture of it. It is based on the light received when you open and close the shutter. What it really would be is Lorentz contracted, and therefore oblate, in the direction of motion. See the links I posted.