Boson Stars in Bumblebee Gravity and Their Gravitational Waveforms from Extreme-Mass-Ratio Inspirals

TL;DR

This paper investigates Lorentz violation in bumblebee gravity and its impact on horizonless mini-boson stars and their gravitational-wave signatures from extreme-mass-ratio inspirals (EMRIs). By solving the modified Einstein–Klein–Gordon system with a nonzero bumblebee field, it shows that the dimensionless parameter $\ell = 2\kappa\xi b^2$ modulates radial pressure and hence the star’s cohesion: positive $\ell$ strengthens binding and yields more compact configurations, while negative $\ell$ promotes diffusion and can eliminate static solutions below a critical value. In EMRIs, test-particle orbits in boson-star backgrounds reveal that $\ell$ shifts orbital properties and generates distinct gravitational-wave morphologies: grazing orbits produce intermittent bursts similar to black-hole EMRIs, whereas penetrating orbits show sustained, amplitude-modulated signals with substantial dephasing and spectral content extending into the LISA band. The study demonstrates that penetrating orbits exhibit observable frequency shifts and modulations in the characteristic strain $h_c(f)$, suggesting that LISA could constrain Lorentz-violating effects in this framework. Overall, the work connects Lorentz-violating gravity, boson-star structure, and low-frequency gravitational-wave observables, offering a pathway to test fundamental symmetries with space-based detectors.

Abstract

We investigate the impact of Lorentz violation on the internal structure of mini-boson stars and the resulting gravitational-wave signals from extreme-mass-ratio inspirals (EMRIs) within the framework of bumblebee gravity. Numerical solutions for static, spherically symmetric configurations reveal that a positive Lorentz-violating parameter $\ell$ suppresses repulsive pressure, thereby enhancing gravitational binding and yielding more compact boson stars. Conversely, a negative $\ell$ amplifies repulsive pressure and weakens gravitational binding, such that no static solutions exist beyond a critical negative value. These structural modifications imprint distinct features on EMRI dynamics, characterized by a monotonic decrease in both orbital eccentricity and radial range as $\ell$ increases. Unlike the intermittent bursts from grazing orbits that resemble black-hole signals, penetrating orbits that enter the boson-star core exhibit sustained, amplitude-modulated gravitational-wave signatures without quiet intervals. Their characteristic strain falls within the detectability range of LISA, providing a potential observable for constraining Lorentz violation.

Figures (11)

• Figure 1: $\phi(r)$, $m(r)$, $n(r)$ and $\sigma(r)$ for different values of the Lorentz-violating parameter $\ell$, with $\omega=0.9$.
• Figure 2: Mass $M$ plotted against the frequency $\omega$ and the Lorentz-violating parameter $\ell$, respectively.
• Figure 3: Particle number $N$ plotted against the frequency $\omega$ and the Lorentz-violating parameter $\ell$, respectively.
• Figure 4: Compactness $C$ and $M_{99}$-$R_{99}$ curves as a function of frequency $\omega$ for different values of the Lorentz-violating parameter $\ell$.
• Figure 5: Binding energy $E_b$ plotted against the frequency $\omega$ for different values of the Lorentz-violating parameter $\ell$.