Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical Behavior in a Massless Scalar Field Collapse with
  Self-interaction Potential   We examine a one-parameter family of analytical solutions representing
spherically symmetric collapse of a nonlinear massless scalar field with
self-interaction in an asymptotically flat spacetime. The time evolution
exhibits a type of critical behavior. Depending on the scalar charge parameter
$q$ as compared to a critical value $q^*$, the incoming scalar wave collapses
either to a globally naked central singularity if $q<q^*$ (weak field) or to a
scalar-hairy black hole if $q>q^*$ (strong field), both having finite
asymptotic masses. Near the critical evolution, the black hole mass follows a
product-logarithmic scaling law: $-M^2\ln M \sim q-q^*$ with $0<M\ll 1$ and
$q>q^*$. The solution admits no self-similarity and satisfies the null and the
strong energy conditions.

2
The categories of this paper are: math
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph