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In a recent thread, the following was posted regarding the "no hair" theorem for black holes:
In the arxiv paper linked to, it says the following (p. 2, after Theorem 1.1):
"Hawking has shown that in addition to the original, stationary, Killing field, which has to be tangent to the event horizon, there must exist, infinitesimally along the horizon and tangent to its generators, an additional Killing vector-field."
This is the first I've heard of this, and it's not elaborated on in the paper. Can anyone explain what this refers to?
martinbn said:Carter and Robinson proved it assuming that the space-time has axial symmetry. Hawking removed that assumption, but had an analyticity, assumption which is unreasonable both mathematically and physically. The problem is still open. In the mathematical literature it is known as the rigidity conjecture.
www.ihes.fr/~vanhove/Slides/Klainerman-ihes-fev2011.pdf
https://arxiv.org/pdf/1501.01587
In the arxiv paper linked to, it says the following (p. 2, after Theorem 1.1):
"Hawking has shown that in addition to the original, stationary, Killing field, which has to be tangent to the event horizon, there must exist, infinitesimally along the horizon and tangent to its generators, an additional Killing vector-field."
This is the first I've heard of this, and it's not elaborated on in the paper. Can anyone explain what this refers to?