In the case of Einstein gravity, one can prove that the NHEK (near-horizon extremal Kerr geometry) is
the unique (up to diffeomorphisms) regular stationary and axisymmetric solution asymptotic to the
NHEK geometry with a smooth horizon [4]. This can be understood as a Birkoff theorem for
the NHEK geometry. This can be paraphrased by the statement that there are no black holes
“inside” of the NHEK geometry. One can also prove that there is a near-horizon geometry
in the class (25
), which is the unique (up to diffeomorphisms) near-horizon stationary and
axisymmetric solution of AdS–Einstein–Maxwell theory [192, 193, 191]. The assumption of
axisymmetry can be further relaxed since stationarity implies axisymmetry [170]. It is then natural to
conjecture that any stationary solution of the more general action (1
), which asymptotes to a
near-horizon geometry of the form (25
) is diffeomorphic to it. This conjecture remains to be
proven.
http://www.livingreviews.org/lrr-2012-11 |
Living Rev. Relativity 15, (2012), 11
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