Boson Stars in AdS

TL;DR

This work investigates the nonlinear dynamics of a complex scalar in global $AdS_4$ by constructing boson-star solutions and analyzing their stability both linearly and nonlinearly. The authors show that, in contrast to the weakly turbulent instability reported for generic AdS perturbations, boson stars are nonlinearly stable under small perturbations, and even broad families of initially dispersed energy do not collapse to black holes. They connect these nonlinear results to oscillon modes in the small-amplitude limit and demonstrate stability through perturbative analyses and full nonlinear evolutions, including “fake” (real) boson-star data. The findings imply that many generic initial conditions in the dual strongly coupled CFT do not thermalize, reshaping the understanding of AdS stability and holographic thermalization. A key insight is that the spectral distribution of initial data in the oscillon basis may govern stability, suggesting a criterion for nonlinear stability in AdS-like spacetimes and motivating further holographic exploration.

Abstract

We construct boson stars in global Anti de Sitter (AdS) space and study their stability. Linear perturbation results suggest that the ground state along with the first three excited state boson stars are stable. We evolve some of these solutions and study their nonlinear stability in light of recent work \cite{Bizon:2011gg} arguing that a weakly turbulent instability drives scalar perturbations of AdS to black hole formation. However evolutions suggest that boson stars are nonlinearly stable and immune to the instability for sufficiently small perturbation. Furthermore, these studies find other families of initial data which similarly avoid the instability for sufficiently weak parameters. Heuristically, we argue that initial data families with widely distributed mass-energy distort the spacetime sufficiently to oppose the coherent amplification favored by the instability. From the dual CFT perspective our findings suggest that there exist families of rather generic initial conditions in strongly coupled CFT (with large number of degrees of freedom) that do not thermalize in the infinite future.

Figures (12)

• Figure 1: (Colour online) Condensate values \ref{['irpert']} and \ref{['uv']} for level $j=\{0,1,2,3\}$ ( $\{$dashed purple, dotted green,dot-dashed blue, solid orange$\}$ curves) boson stars. The red lines represent perturbative in $p_0^h$ approximations, see Table \ref{['table1']}.
• Figure 2: (Colour online) Mass vs. $p_0^h$ (left panel) and vs. charge (right panel) for level $j=\{0,1,2,3\}$ ( $\{$dashed purple, dotted green,dot-dashed blue, solid orange$\}$ curves) boson stars. The solid red lines represent perturbative in $Q$ approximations, see \ref{['mql']}.
• Figure 3: (Colour online) Spectral decomposition of level $j=\{0,1,2,3\}$ ($\{$purple circles,green triangles,blue squares,orange diamonds$\}$) boson stars in oscillon basis, see \ref{['os3']}. For large $i$ all the curves approach a universal fall-off $c_i^{(j)}\propto (1+i)^{-6}$ (the black dashed curve).
• Figure 4: (Colour online) Spectrum of linearized fluctuations about $j=0$ boson stars as a function of $p_0^h$ (black dots). The dashed orange/solid red curves are successive approximations to $\chi^2=\left(\chi(p_0^h\equiv\lambda)\right)^2$ in $\lambda^2$, see \ref{['seriesg1f1']}.
• Figure 5: (Colour online) Collapse times for Gaussian perturbations of a ground state boson star ($\phi_1(0,0)=0.253$) and its corresponding fake star. Increasing resolutions are shown. For short collapse times, resolutions agree. However, for the longest evolutions, higher resolutions are needed. Even with very high resolutions, small $\epsilon$ evolutions show no sign of collapse.