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Numerical studies of Phi^2-Oscillatons
General Relativity and Quantum Cosmology · Submitted 24 Jan 2003
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim On the other hand, U-oscillatons are intrinsically unstable: they migrate to the S-branch if their mass is decreased and collapse to black holes if their mass is increased even by a small amount.
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The abstract, sentence by sentence
We present an exhaustive analysis of the numerical evolution of the Einstein-Klein-Gordon equations for the case of a real scalar field endowed with a quadratic self-interaction potential. The self-gravitating equilibrium configurations are called oscillatons and are close relatives of boson stars, their complex counterparts. Unlike boson stars, for which the oscillations of the two components of the complex scalar field are such that the spacetime geometry remains static, oscillatons give rise to a geometry that is time-dependent and oscillatory in nature. However, they can still be classified into stable (S-branch) and unstable (U-branch) cases. We have found that S-oscillatons are indeed stable configurations under small perturbations and typically migrate to other S-profiles when perturbed strongly. On the other hand, U-oscillatons are intrinsically unstable: they migrate to the S-branch if their mass is decreased and collapse to black holes if their mass is increased even by a small amount. The S-oscillatons can also be made to collapse to black holes if enough mass is added to them, but such collapse can be efficiently prevented by the gravitational cooling mechanism in the case of diluted oscillatons.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present an exhaustive analysis of the numerical evolution of the Einstein-Klein-Gordon equations for the case of a real scalar field endowed with a quadratic self-interaction potential. | contribution 0.99 | 0.94 | 0.05 | asserted 0.98 |
| s1 | The self-gravitating equilibrium configurations are called oscillatons and are close relatives of boson stars, their complex counterparts. | background 1.00 | 0.07 | 0.04 | asserted 1.00 |
| s2 | Unlike boson stars, for which the oscillations of the two components of the complex scalar field are such that the spacetime geometry remains static, oscillatons give rise to a geometry that is time-dependent and oscillatory in nature. | background 0.91 | 0.17 | 0.05 | asserted 1.00 |
| s3 | However, they can still be classified into stable (S-branch) and unstable (U-branch) cases. | background 0.46 | 0.27 | 0.09 | asserted 0.94 |
| s4 | We have found that S-oscillatons are indeed stable configurations under small perturbations and typically migrate to other S-profiles when perturbed strongly. | result 1.00 | 0.94 | 0.22 | asserted 1.00 |
| s5 | On the other hand, U-oscillatons are intrinsically unstable: they migrate to the S-branch if their mass is decreased and collapse to black holes if their mass is increased even by a small amount. | result 1.00 | 0.89 | 0.30 | asserted 1.00 |
| s6 | The S-oscillatons can also be made to collapse to black holes if enough mass is added to them, but such collapse can be efficiently prevented by the gravitational cooling mechanism in the case of diluted oscillatons. | result 0.99 | 0.76 | 0.17 | asserted 0.70 |
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The paper
Original abstract
We present an exhaustive analysis of the numerical evolution of the Einstein-Klein-Gordon equations for the case of a real scalar field endowed with a quadratic self-interaction potential. The self-gravitating equilibrium configurations are called oscillatons and are close relatives of boson stars, their complex counterparts. Unlike boson stars, for which the oscillations of the two components of the complex scalar field are such that the spacetime geometry remains static, oscillatons give rise to a geometry that is time-dependent and oscillatory in nature. However, they can still be classified into stable (S-branch) and unstable (U-branch) cases. We have found that S-oscillatons are indeed stable configurations under small perturbations and typically migrate to other S-profiles when perturbed strongly. On the other hand, U-oscillatons are intrinsically unstable: they migrate to the S-branch if their mass is decreased and collapse to black holes if their mass is increased even by a small amount. The S-oscillatons can also be made to collapse to black holes if enough mass is added to them, but such collapse can be efficiently prevented by the gravitational cooling mechanism in the case of diluted oscillatons.
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References
How the literature uses it
34 arXiv papers cite this in 73 sentences
Papers citing it · 36 sentences without a confident label
Builds on it 1 paper
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In this section we will show that the same solutions already obtained in [ref] imply that string moduli potentials support star-like solutions in the dilute regime.
Moduli Stars · Moduli Stars · 0.93
Uses its method or tool 10 papers
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Following the analysis done in [ref] , we calculate the power spectrum of the evolution for the entire S-branch; we show in Fig. [ref] the quasi-normal frequency $f$ as a function of the total mass $M_T$.
$\Phi^{4}$ Oscillatons · S-branch and Quasi-normal Modes · 0.97
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The axion star initial set up is built following Refs. [ref] , while the implementation of the electromagnetic field follows the methodology introduced in Refs. [ref] .
Multimessenger signals from compact axion star mergers · Theory · 1.00
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[equation] following the method used in Ref. [ref] .
Electromagnetic instability of compact axion stars · Introduction · 1.00
Uses its data or values 1 paper
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The transition between the two branches occurs at the critical mass $M_c = 0.605 m_Pl^2/μ$ of compactness $C = 0.14$ [ref] .
Boson Stars and Oscillatons: A Review · Real scalar fields · 0.93
Compares with it 3 papers
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The Bondi mass is in very good agreement with the results of the 3+1 approach, where the critical ADM mass is $M_ADM≈15.2 M_p^2m^-1$ (after accounting for the switch from Planck mass to reduced Planck mass) [ref] .
Relativistic collapse of axion stars · Numerical results · 1.00
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Our results are similar to results found for boson stars [ref] , oscillatons [ref] , and Proca stars [ref] .
Perturbing the ground state of Dirac stars · Introduction · 1.00
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Figure [ref](c) looks very similar to figures found in related studies [ref] and, just as in those studies, we conclude that our system is migrating to the stable region.
Dynamical evolution of fermion-boson stars with realistic equations of state · Weak perturbations · 0.94
Cites it as background 14 papers
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The fully relativistic collapse of a massive scalar field was studied in some detail using null coordinates in Ref. [ref] and using a 3+1 approach in Ref. [ref] .
Relativistic collapse of axion stars · Numerical results · 0.83
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Oscillatons are non-singular and asymptotically flat solutions of the Einstein-Klein-Gordon (EKG) equations, in which both metric and scalar field are fully time-dependent [ref] .
$\Phi^{4}$ Oscillatons · Introduction · 0.98
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In the absence of a global U(1) symmetry, the field cannot maintain a static phase; instead, the entire configuration oscillates coherently at a fundamental frequency slightly below the particle mass, giving rise to long-lived, nonsingular, asymptotically-flat solutions known as oscillatons [ref] .
Periodic Gravitational Lensing with Oscillating Boson Stars · Introduction · 0.91
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