What I love about the hairy ball theorem is that it shows how geometry enforces limits without dynamics. No matter how carefully you try to smooth things out locally, the global structure has the final word.
For black holes, we have the “no hair theorem,” but a quasar and the radiation emitted from an accretion disk eerily match the poles of the hairy ball theorem for a sphere rotating in one direction. Stars before they collapse into a black hole have spin angular momentum. Neutron stars are electrically neutral before the black hole forms. Where does the rest of the stars' information, the entropy, go?
Does it go out of the poles due to the hairy ball theorem?
Wow, this is great! I had no idea the hairy ball theorem had so many applications. I used to not really care about such things but now that I'm teaching time I can see that they serve a pedagogical purpose.
Welcome to Substack! Let’s connect and share ideas! I’m sure there are many interesting things ahead on your writing journey.Please support my latest post! I’d be happy to return the favor and comment on your work.
What I love about the hairy ball theorem is that it shows how geometry enforces limits without dynamics. No matter how carefully you try to smooth things out locally, the global structure has the final word.
For black holes, we have the “no hair theorem,” but a quasar and the radiation emitted from an accretion disk eerily match the poles of the hairy ball theorem for a sphere rotating in one direction. Stars before they collapse into a black hole have spin angular momentum. Neutron stars are electrically neutral before the black hole forms. Where does the rest of the stars' information, the entropy, go?
Does it go out of the poles due to the hairy ball theorem?
Wow, this is great! I had no idea the hairy ball theorem had so many applications. I used to not really care about such things but now that I'm teaching time I can see that they serve a pedagogical purpose.
do you think allowing self intersections makes it easy???
Gold 😆
Welcome to Substack! Let’s connect and share ideas! I’m sure there are many interesting things ahead on your writing journey.Please support my latest post! I’d be happy to return the favor and comment on your work.