Formation of a condensate during charged collapse

TL;DR

This paper demonstrates through numerical simulations that a charged scalar condensate can form inside a black hole during gravitational collapse, exhibiting spontaneous gauge symmetry breaking without a traditional potential.

Contribution

It provides the first numerical evidence of condensate formation in a massless charged scalar field collapsing into a black hole in asymptotically flat spacetime, without a symmetry-breaking potential.

Findings

Condensate forms with a non-zero scalar field magnitude inside the black hole.

Scalar field rotation in the complex plane matches electric potential within 1%.

Supports previous analytical results in AdS backgrounds, now in flat spacetime.

Abstract

We observe a condensate forming in the interior of a black hole (BH) during numerical simulations of gravitational collapse of a massless charged (complex) scalar field. The magnitude of the scalar field in the interior tends to a non-zero constant; spontaneous breaking of gauge symmetry occurs and a condensate forms. This phenomena occurs in the presence of a BH without the standard symmetry breaking quartic potential; the breaking occurs via the dynamics of the system itself. We also observe that the scalar field in the interior rotates in the complex plane and show that it matches numerically the electric potential to within $1\%$. That a charged scalar condensate can form near the horizon of a black hole in the Abelian Higgs model without the standard symmetry breaking potential had previously been shown analytically in an explicit model involving a massive scalar field in an $AdS_4$ background. Our numerical simulation lends strong support to this finding, although in our case the scalar field is massless and the spacetime is asymptotically flat.