Fermionic $\theta$ Vacua and Long-Necked Remnants

TL;DR

This paper investigates how vacuum polarization effects in certain extremal black hole backgrounds influence spacetime geometry, revealing that finite fermion mass and vacuum angle $ heta$ can create horizons that close off infinite necks, with implications for black hole physics.

Contribution

It demonstrates that vacuum polarization due to finite mass fermions in dilatonic extremal black holes significantly alters the geometry, especially near horizons, depending on fermion mass and $ heta$ angle.

Findings

Vacuum energy density affects black hole neck structure.

Finite fermion mass can induce horizons at finite distances.

Results are qualitatively robust despite strong coupling.

Abstract

We study a vacuum polarization effect in the background of certain dilatonic extremal black hole, known as the cornucopion. Whenever the charged fermions are of any finite mass, the gravitational backreaction to a generic value of a $CP$ nonconserving vacuum angle $\theta$ is shown to be important owing to a vacuum energy density which does not vanish deep inside the cornucopion. When this energy density is positive, this effect creates an extremal horizon at finite physical distance, closing off the infinite neck. We study the geometry near this horizon in some detail and find different physical interpretations for small and large fermion mass. Also, we argue that the conclusion is qualitatively correct despite the strong coupling.