Stability of relativistic stars with scalar hairs

Understand

We study the stability of relativistic stars in scalar-tensor theories with a nonminimal coupling of the form $F(\phi)R$, where $F$ depends on a scalar field $\phi$ and $R$ is the Ricci scalar.

• On a spherically symmetric and static background, we incorporate a perfect fluid minimally coupled to gravity as a form of the Schutz-Sorkin action.
• The odd-parity perturbation for the multipoles $l \geq 2$ is ghost-free under the condition $F(\phi)>0$, with the speed of gravity equivalent to that of light.
• For even-parity perturbations with $l \geq 2$, there are three propagating degrees of freedom arising from the perfect-fluid, scalar-field, and gravity sectors.