Various papers¹ have been written about the Taub-NUT or Kerr-Taub-NUT exact solutions to Einstein's equations, but while they describe mathematically precise (local or global) properties of that spacetime, none of them seems to discuss its physics in a qualitative and intuitive way, and I find myself still unable to form any intuitive understanding of what the NUT parameter “means” (except for a very vague idea that “it is to mass like magnetic charge is to electric charge”, which is not really helpful) or what its physical effects are.
For example, there are many places discussing what the physical effects of a Kerr black hole are, what an observer would see under various conditions, what its geometry looks like, stuff like this (I have myself produced raytraced images of Kerr black holes, and videos of falling inside them, etc.). But there does not appear to be anything remotely similar for the Taub-NUT or Kerr-Taub-NUT solutions. What would someone encountering such a “black hole” (I'm not even completely sure we should call them “black holes” at all) see? How would they know they're dealing with this kind of black hole?
And specifically, here's one more precise question: how do we know the supermassive black hole at the center of the Milky Way has zero NUT parameter? (Do we know this? Or what bounds can we give on its NUT parameter?) What experiment could we do, either in real world, or assuming we could approach it, to test this? What would the qualitative effect of a nonzero NUT parameter look like?
(And here's another one, for fun: what would be the effect of the solar system encountering an object with a small mass but fairly large NUT parameter?)
Is someone able to shed light on such questions in a way that would help me get an intuitive grasp on the meaning of this elusive parameter, and its possible existence or nonexistence in the Universe?
- E.g.: Misner, “Taub-NUT space as a counterexample to almost anything”, Miller, “Global analysis of the Kerr‐Taub‐NUT metric”, Al-Badawi & Halilsoy, “On the physical meaning of the NUT parameter”, Pradhan, “Circular Orbits in the Taub-NUT and mass-less Taub-NUT Space-time”, Vandeev & Semenova “Geodesic deviation on symmetry axis in Taub-NUT metric” and many others. Also, §5.8 in Hawking & Ellis, The large scale structure of space-time.
