Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetric inequality for higher-dimensional black holes   The initial data sets for the five-dimensional Einstein equation have been
examined. The system is designed such that the black hole ($\simeq S^3$) or the
black ring ($\simeq S^2\times S^1$) can be found. We have found that the
typical length of the horizon can become arbitrarily large but the area of
characteristic closed two-dimensional submanifold of the horizon is bounded
above by the typical mass scale. We conjecture that the isoperimetric
inequality for black holes in $n$-dimensional space is given by $V_{n-2}
\lesssim GM$, where $V_{n-2}$ denotes the volume of typical closed
$(n-2)$-section of the horizon and $M$ is typical mass scale, rather than
$C\lesssim (GM)^{1/(n-2)}$ in terms of the hoop length $C$, which holds only
when $n=3$.

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The categories of this paper are: supr-con
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess