Exotic compact objects in Einstein-scalar-Maxwell theories

In k-essence theories within general relativity, where the matter Lagrangian depends on a real scalar field $\phi$ and its kinetic term $X$, static and spherically symmetric compact objects with a positive-definite energy density cannot exist without introducing ghosts. We show that this no-go theorem can be evaded when the k-essence Lagrangian is extended to include a dependence on the field strength $F$ of a $U(1)$ gauge field, taking the general form ${\cal L}(\phi, X, F)$. In Einstein-scalar-Maxwell theories with a scalar-vector coupling $\mu(\phi) F$, we demonstrate the existence of asymptotically flat, charged compact stars whose energy density and pressure vanish at the center. With an appropriate choice of the coupling function $\mu(\phi)$, we construct both electric and magnetic compact objects and derive their metric functions and scalar- and vector-field profiles analytically. We compute their masses and radii, showing that the compactness lies in the range ${\cal O}(0.01)<{\cal C}<{\cal O}(0.1)$. A linear perturbation analysis reveals that electric compact objects are free of strong coupling, ghost, and Laplacian instabilities at all radii for $\mu(\phi)>0$, while magnetic compact objects suffer from strong coupling near the center.