Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pointlike electric charge in gravitational field theory   The existence of charged elementary 'point particles' still is a basically
unsolved puzzle in theoretical physics. The present work takes a fresh look at
the problem by including gravity---without resorting to string theory. Using
Einstein's equations for the gravitational fields in a general static isotropic
metric with the full energy-momentum tensor (for the charged material mass and
the electromagnetic fields) as the source term, a novel exact solution with a
well-defined characteristic radius emerges where mass and charge accumulate:
$r_{\rm c}{=}\sqrt{r_{\rm e}r_o/2}$---with $r_{\rm
e}{=}Q^2\!/4\pi\epsilon_omc^2$ being the 'classical' radius associated with the
total charge $Q$ and where $r_o{=}2mG/c^2$ is the Schwarzschild radius
belonging to the observable mass $m$ (for the electron one has $r_{\rm
e}{\approx}10^{-15}$m and $r_o{\approx}\,10^{-57}$m). The resulting
'Einstein-Maxwell' gravitational electron radius can also be written as $r_{\rm
c}{=}\ell_{\rm P}\sqrt{\alpha_{\rm e}}$, where $\ell_{\rm P}{=}\sqrt{\hbar
G/c^3}{\approx}10^{-35}$m is the fundamental Planck length and $\alpha_{\rm
e}{=}e^2\!/4\pi\epsilon_o\hbar c{\approx}1/137$ the fine-structure constant,
which yields $r_{\rm c}^{\rm electron}{=}1.38063{\times}10^{-36}$m.

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The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga