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Numerical simulation of oscillatons: Extracting the radiating tail

Abstract : Spherically symmetric, time-periodic oscillatons---solutions of the Einstein-Klein-Gordon system (a massive scalar field coupled to gravity) with a spatially localized core---are investigated by very precise numerical techniques based on spectral methods. In particular, the amplitude of their standing-wave tail is determined. It is found that the amplitude of the oscillating tail is very small, but nonvanishing for the range of frequencies considered. It follows that exactly time-periodic oscillatons are not truly localized, and they can be pictured loosely as consisting of a well (exponentially) localized nonsingular core and an oscillating tail making the total mass infinite. Finite mass physical oscillatons with a well localized core---solutions of the Cauchy-problem with suitable initial conditions---are only approximately time-periodic. They are continuously losing their mass because the scalar field radiates to infinity. Their core and radiative tail is well approximated by that of time-periodic oscillatons. Moreover the mass loss rate of physical oscillatons is estimated from the numerical data and a semiempirical formula is deduced. The numerical results are in agreement with those obtained analytically in the limit of small amplitude time-periodic oscillatons.
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Philippe Grandclément, Gyula Fodor, Péter Forgács. Numerical simulation of oscillatons: Extracting the radiating tail. Physical Review D, American Physical Society, 2011, 84, pp.65037. ⟨10.1103/PhysRevD.84.065037⟩. ⟨hal-03724122⟩



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