Neutron stars with a generalized Proca hair and spontaneous vectorization
Ryotaro Kase, Masato Minamitsuji, Shinji Tsujikawa
Abstract
In a class of generalized Proca theories, we study the existence of neutron star solutions with a nonvanishing temporal component of the vector field ${A}_{\ensuremath{\mu}}$ approaching 0 toward spatial infinity, as they may be the endpoints of tachyonic instabilities of neutron star solutions in general relativity with ${A}_{\ensuremath{\mu}}=0$. Such a phenomenon is called spontaneous vectorization, which is analogous to spontaneous scalarization in scalar-tensor theories with nonminimal couplings to the curvature or matter. For the nonminimal coupling $\ensuremath{\beta}XR$, where $\ensuremath{\beta}$ is a coupling constant and $X=\ensuremath{-}{A}_{\ensuremath{\mu}}{A}^{\ensuremath{\mu}}/2$, we show that there exist both 0-node and 1-node vector-field solutions, irrespective of the choice of the equations of state of nuclear matter. The 0-node solution, which is present only for $\ensuremath{\beta}=\ensuremath{-}\mathcal{O}(0.1)$, may be induced by some nonlinear effects such as the selected choice of initial conditions. The 1-node solution exists for $\ensuremath{\beta}=\ensuremath{-}\mathcal{O}(1)$, which suddenly emerges above a critical central density of star and approaches the general relativistic branch with the increasing central density. We compute the mass $M$ and radius ${r}_{s}$ of neutron stars for some realistic equations of state and show that the $M\ensuremath{-}{r}_{s}$ relations of 0-node and 1-node solutions exhibit a notable difference from those of scalarized solutions in scalar-tensor theories. Finally, we discuss the possible endpoints of tachyonic instabilities.