Exotic compact objects in Einstein-scalar-Maxwell theories

Abstract

In k-essence theories within general relativity, where the matter Lagrangian depends on a real scalar field $φ$ 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 ${\cal L}(φ, X, F)$. In Einstein-scalar-Maxwell theories with a scalar-vector coupling $μ(φ) F$, 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 $μ(φ)$, 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 $μ(φ)>0$, while magnetic compact objects suffer from strong coupling near the center.

Figures (7)

• Figure 1: Metric components $f$ and $h$ as functions of $x=r/r_0$ for $N_0=0.5$. We also show the mass function ${\cal M}$, which is normalized by $M_0=M_{\rm Pl}^2 r_0$.
• Figure 2: Profiles of $\tilde{q}_E A_0'$, $\phi'$, and $\phi-\phi_0$ as functions of $x=r/r_0$ for $N_0=0.5$. Each quantity is normalized by $M_{\rm Pl}/r_0$, $M_{\rm Pl}/r_0$, and $M_{\rm Pl}$, respectively.
• Figure 3: Profiles of $\rho$, $P_r$, $\hat{\rho}$, and $\hat{P}_r$ as functions of $r/r_0$ for $N_0=0.5$. All of these quantities are normalized by $M_{\rm Pl}^2/r_0^2$.
• Figure 4: The rescaled coupling $\mu_E=\tilde{q}_E^{-2}\mu$ as a function of $\phi-\phi_0$ (normalized by $M_{\rm Pl}$) with three different values of $N_0$.
• Figure 5: The ADM mass $M$ is plotted against the object's radius $r_s$, where $M$ and $r_s$ are normalized by $M_0 = M_{\rm Pl}^2 r_0$ and $r_0$, respectively. The solid and dashed lines represent the cases where the radius is determined by the conditions ${\cal M}(r_s) = 0.99M$ and ${\cal M}(r_s) = 0.90M$, respectively. The black dots along both the solid and dashed lines correspond to the cases with $N_0 = 0.1$, $0.5$, and $0.9$.