### 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.

Original language | English |
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Article number | 065037 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 84 |

Issue number | 6 |

DOIs | |

Publication status | Published - Sep 30 2011 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Numerical simulation of oscillatons : Extracting the radiating tail.** / Grandclément, Philippe; Fodor, G.; Forgács, P.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 84, no. 6, 065037. https://doi.org/10.1103/PhysRevD.84.065037

}

TY - JOUR

T1 - Numerical simulation of oscillatons

T2 - Extracting the radiating tail

AU - Grandclément, Philippe

AU - Fodor, G.

AU - Forgács, P.

PY - 2011/9/30

Y1 - 2011/9/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80053899503&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.84.065037

DO - 10.1103/PhysRevD.84.065037

M3 - Article

AN - SCOPUS:80053899503

VL - 84

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 6

M1 - 065037

ER -