ENERGY LOSS RATE OF OSCILLATONS

According to numerical simulations, general relativistic massive real scalar fields can form extremely long living oscillating localized objects, called oscillating soliton stars or oscillatons. We present a small-amplitude expansion to describe the core region of these configurations. To leading order we obtain the Schrodinger-Newton equations. However, the small-amplitude expansion is only an asymptotic one, and consequently misses a nonperturbatively small oscillating tail which is responsible for a tiny energy loss of oscillatons, making them non-exactly periodic. The energy loss rate is calculated by complex extension of the Fourier mode equations and applying Borel summation.