Oscillating soliton stars

We study a new type of self-gravitating object, described by a soliton solution to the coupled system of the Einstein equation and a matter field equation. The solution describing the self-gravitating object is not static but, instead, is periodic, with both the spacetime geometry and the matter field oscillating in time. In particular, we show that a system described by a real scalar field ${\mathit{g}}^{\mathrm{\mu }\nu }$ ${\mathrm{\phi }}_{;\mathrm{\mu }\nu }$-${\mathit{m}}^2$φ=0 admits such a solution, which is stable under perturbations. The existence of such objects could have important implications for astrophysics and cosmology.