Boson Stars in $D \ge 4$ Dimensions: Stability, Oscillation Frequencies, and Dynamical Evolutions

TL;DR

The paper investigates spherically symmetric boson stars in $D \ge 4$ and addresses radial stability in higher dimensions by combining a dimensionally general perturbative pulsation analysis with nonlinear spherical evolutions. It shows that radially stable branches exist in $D=5$ and $D=6$ for massive (quartic) potentials and in $D=5$ for solitonic potentials, while $D=6$ solitons remain unstable; nonlinear evolutions confirm that linear stability predictions extend to the full nonlinear spherical dynamics, including metastable cases with positive binding energy. The results broaden the landscape of higher-dimensional horizonless compact objects, demonstrate the viability of NR methods with a modified cartoon approach in higher dimensions, and highlight the nuanced role of binding energy in predicting stability. These findings have potential implications for critical phenomena, stress-energy configurations, and gravitational dynamics in higher-dimensional theories. The work also outlines future directions, including nonradial stability analyses and explorations within alternative theories of gravity or larger dimensionalities.

Abstract

We construct spherically symmetric boson star solutions in $D \in \{4,5,6\}$ spacetime dimensions, considering the effects of both a quartic self-interaction term and a solitonic potential. We then perform a perturbative analysis, generalizing the pulsation equations to arbitrary dimension and potential and hence demonstrating the existence of radially stable higher-dimensional boson star solutions. We supplement these linear results with perturbed and unperturbed nonlinear dynamical evolutions in spherical symmetry, obtained using a dimensional reduction that allows us to evolve spacetimes with any number of background dimensions using the same numerical framework, while preserving the full gauge freedom of standard approaches to numerical relativity. The results of these evolutions indicate that the solutions we identify as perturbatively stable are indeed generally stable to nonlinear spherical dynamics.

Figures (14)

• Figure 1: Mass against radius curves for a selection of BS families, showing the impact of the spacetime dimension. For massive models, $\hat{\lambda} := \lambda / \mu^2 .$
• Figure 2: Radius (left) and binding energy (right) against amplitude for solitonic families in $D = 6$, showing the divergence in $r_{99}$ at sufficiently large central amplitude even as the binding energy approaches a limiting value.
• Figure 3: Compactness (defined in Eq. \ref{['eq:C_def']}) against central amplitude for solitonic families in $D = 4$ (left) and $5$ (right) dimensions.
• Figure 4: Bifurcation diagrams for representative mini, massive, and solitonic solution families in $D = 5$ spacetime dimensions. As a visual aid, we indicate the limiting solution as $A_0 \rightarrow 0$ with a blue dot.
• Figure 5: Fundamental radial oscillation frequency $\chi_0^2$ against central amplitude $A_0$ for mini, massive, and solitonic BS models in varying dimension. Regions with $\chi_0^2 > 0$ correspond to linear radial stability. Inset on the bottom panel shows the first stable branch in $D = 4$, which is absent in $D = 5$, as well as the result for $D = 6$. Notice $\chi_0^2 \rightarrow 0$ as the solution family diverges in the $D = 6$ case.