Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal Isolated Horizons: A Local Uniqueness Theorem   We derive all the axi-symmetric, vacuum and electrovac extremal isolated
horizons. It turns out that for every horizon in this class, the induced metric
tensor, the rotation 1-form potential and the pullback of the electromagnetic
field necessarily coincide with those induced by the monopolar, extremal
Kerr-Newman solution on the event horizon. We also discuss the general case of
a symmetric, extremal isolated horizon. In particular, we analyze the case of a
two-dimensional symmetry group generated by two null vector fields. Its
relevance to the classification of all the symmetric isolated horizons,
including the non-extremal once, is explained.

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The categories of this paper are: math
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
23
The categories of this paper are: solv-int