I’m reading a magazine about “extreme physics”. In the section on singularities, naked v. non naked. There’s a mention of inhogemity, below a certain threshold, a black hole, above, a naked singularity. The article never articulated the threshold, so do any Dopers have a clarification for me?
I’ve never seen it expressed in terms of inhomogeneity. My best guess is that the article was talking about spinning black holes, which are anisotropic, but all black holes are inhomogeneous. If the angular momentum divided by the mass squared (and times appropriate powers of c and G to make the units work out) is less than one, the singularity is decently clad in an event horizon, while if it’s bigger than one, it’s naked. It’s expected that this parameter (called the dimensionless angular momentum) is typically about .95 or larger for most black holes in the Universe, but don’t worry, there is no physical process known by which it can go from less than 1 to greater than 1.
You can also have a black hole that’s extreme (that is, its singularity is naked) by virtue of excessive electric charge, or magnetic charge, or an appropriate combination of all three. Again, though, so far as we know there’s no way to actually get there from here.
Hmm, I guess you mean anistropy rather than inhomogeneity.
If the angular momentum parameter divided by the mass parameter in the Kerr solution is taken as a measure of its anistropy, then above a certain threshold Kerr solutions represent naked singularities (and are generally assumed to be unphysical). The exact value of this threshold depends on units, but in natural units the threshold would be 1.
Beaten by Chronos
Thanks Chronos! I just used the terms they used. Scientific American published it, btw.
Scientific American has gone way downhill in the past couple of decades. I’m saddened but unfortunately not surprised that they would make a mistake like that.