Roy Kerr found a beautiful solution to the Einstein equation 49 years ago. He long deserves a Nobel Prize. The recent Telemach theorem (in print in the African Journal of Mathematics) modifies the appearance of every solution \u201cclose\u201d to a black hole\u2019s horizon. <\/p>\n
What Dieter Fr\u00f6hlich discovered in yesterday\u2019s chaos course at the University of T\u00fcbingen started out from the fact that every rotating black hole has a nonrotating horizon owing to the infinite local slowdown of time. We had concluded before that the in-spiraling trajectories must form something like a \u201cReeb foliation\u201d on the way to the unmoving horizon. He suddenly realized that an \u201canchored rotating Reeb foliation\u201d is the answer. <\/p>\n
I repeat: We had conjectured before that In between the outer unstable limit cycle of in-spiraling trajectories and the inner motionless horizon, there exists a \u201ccircular chain of cups\u201d \u2013 non-crossing trajectories that in a U-turn-like fashion connect the two limiting trajectories (the unstable outer limit cycle and the stable inner limit cycle of opposite orientation). Such a beautiful differential-topological flow was discovered in 1952 by Georges Reeb (as had been pointed out to me by Art Winfree). <\/p>\n
However, the problem is that the attractive inner limit cycle has rotation rate zero. Does this not destroy all hope for consistency? Fr\u00f6hlich saw the solution in a flash: Put the standard Reeb foliation into a rapidly spinning motion, which makes no qualitative difference. Then smoothly reduce the cups\u2019 rotation rate until the attractive inner limit cycle becomes a singular spiky (\u201cstar-node related\u201d) limit cycle while the ring of \u201ccups within cups\u201d retains a constant rotation rate. The obtained \u201canchored rotating Reeb foliation\u201d (anchored everywhere on the horizon) represents a new differential-topological prototype, embraced by nature. <\/p>\n
It would be marvelous to get a response from Professor Kerr himself. (For J.O.R.) <\/p>\n","protected":false},"excerpt":{"rendered":"
Roy Kerr found a beautiful solution to the Einstein equation 49 years ago. He long deserves a Nobel Prize. The recent Telemach theorem (in print in the African Journal of Mathematics) modifies the appearance of every solution \u201cclose\u201d to a black hole\u2019s horizon. What Dieter Fr\u00f6hlich discovered in yesterday\u2019s chaos course at the University of [\u2026]<\/p>\n","protected":false},"author":145,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12,48],"tags":[],"class_list":["post-3039","post","type-post","status-publish","format-standard","hentry","category-existential-risks","category-particle-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/3039","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/145"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=3039"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/3039\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=3039"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=3039"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=3039"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}