Highly compact Proca stars with quartic self-interactions

TL;DR

This paper investigates new self-gravitating Proca star solutions with a novel quartic self-interaction, revealing their potential for extreme compactness and photon sphere formation, but also highlighting associated ghost instabilities.

Contribution

It introduces a new quartic self-interaction for Proca stars, analyzing its effects on star properties and stability, which was not explored in previous studies.

Findings

Proca stars can become highly compact, forming photon spheres.

The quartic self-interaction influences the stability and structure of Proca stars.

Ghost instabilities arise near the compactness threshold for photon sphere formation.

Abstract

We study self-gravitating bound states of a complex vector field, known as Proca stars, with a new type of quartic-order self-interaction which does not exist in the case of either a complex scalar field or a real vector field. Depending on the sign of the coupling constant, this quartic self-interaction can yield a distinct feature of Proca stars from the previously investigated self-interaction of the vector field. We find that self-gravitating solutions can be so compact that the photon sphere could form. However, we also show that the self-interaction gives rise to a ghost instability for the stars whose compactness is close that for the formation of a photon sphere, which might invalidate the formation of the photon sphere.