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.
Cite
@article{arxiv.2212.07659,
title = {Highly compact Proca stars with quartic self-interactions},
author = {Katsuki Aoki and Masato Minamitsuji},
journal= {arXiv preprint arXiv:2212.07659},
year = {2023}
}