Exotic compact objects in Einstein-scalar-Maxwell theories

TL;DR

This paper demonstrates the existence of charged, asymptotically flat compact stars in Einstein-scalar-Maxwell theories by extending k-essence models to include gauge field dependence, overcoming previous no-go theorems.

Contribution

It introduces a new class of charged compact objects in Einstein-scalar-Maxwell theories with explicit scalar-vector coupling, providing analytical solutions and stability analysis.

Findings

Existence of asymptotically flat charged compact stars with vanishing central energy density.

Analytical expressions for metric, scalar, and vector fields of the compact objects.

Stable electric compact objects free of instabilities for positive coupling functions.

Abstract

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.