Note on the charged boson stars with torsion-coupled field

Within the framework of the extended teleparallel gravity, a new class of boson stars has recently been constructed by introducing the nonminimal coupling of the scalar field to the torsion scalar. An interesting feature of these static, spherical, self-gravitating configurations of the massive complex scalar field is their central region with outwardly increasing energy density, surrounded by a thick shell within which the joining with the usual asymptotically Schwarzschild tail takes place. In this work we extend the original model with the $U(1)$ gauge field and we find that the combined effect of the charge and coupling of the field to torsion leads to a significant increase of the maximal mass and the particle number that can be supported against gravity. We also show that some charged configurations preserve the property of having the outwardly increasing energy density over the central region, regardless of the fact that charging the configurations affects the anisotropy of the pressures in the opposite way relative to that of the field-to-torsion coupling terms.

Figure 1

Mass (solid lines in units $M_{\mathrm{Pl}}^2/\mu$) and particle number (dashed lines in units $M_{\mathrm{Pl}}^2/{\mu }^2$) of boson stars with parameters given in Table 1 and for a range of values of ${\sigma }_0=k^{-1/2}\varphi (0)$. Critical configurations are indicated with vertical lines and letters.

Figure 2

Energy-momentum components of the critical configurations A–D (see Table 1 for parameters): energy density (solid thin line) relative to the central energy density ${\rho }_0$, radial and transverse pressure (solid and dashed pair of thin lines) relative to ${\rho }_0$, and the anisotropy (gray thick line) relative to ${\rho }_0$ and scaled up by a factor for clarity.