Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spacetime metric from linear electrodynamics   The Maxwell equations are formulated on an arbitrary (1+3)-dimensional
manifold. Then, imposing a (constrained) linear constitutive relation between
electromagnetic field $(E,B)$ and excitation $({\cal D},{\cal H})$, we derive
the metric of spacetime therefrom.

31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess