Detecting Black hole surrounded by perfect fluid dark matter in Kalb-Ramond fields using quasinormal modes

Abstract

This paper investigates the characteristics of quasinormal modes (QNMs) of static, spherically symmetric black holes under the combined influence of spontaneous Lorentz symmetry breaking (LSB) induced by the Kalb-Ramond (KR) field and perfect fluid dark matter (PFDM). Using M87$^\ast$ shadow data from the Event Horizon Telescope (EHT), we constrain the LSB factor $τ$ and PFDM parameter $ζ$ at 1$σ$ confidence. By combining the sixth-order WKB approximation method with timedomain numerical integration, we systematically compute the complex frequency spectrum of QNMs for black holes in this spacetime background. The numerical results reveal an intriguing conclusion: as the LSB factor $τ$ or the PFDM parameter $ζ$ increases, both the real part and the absolute value of the imaginary part of the QNMs frequencies exhibit a monotonic increase, demonstrating a unique "stiffening" effect. This characteristic stands in stark contrast to the decreasing trend of QNMs frequencies observed in models that consider only traditional dark matter, revealing the critical influence of the coupling between the KR field and PFDM on the dynamic evolution of black holes. This study not only enriches and deepens the understanding of black hole perturbation theory within the framework of modified gravity but also, by identifying the distinctive spectral features of QNMs, offers the potential to distinguish whether the KR field and dark matter are coupled in future observations. Thus, it provides a theoretical foundation for testing mechanisms of spacetime symmetry breaking beyond the standard model and for exploring the nature of dark matter.

Figures (7)

• Figure 1: Shows the variation of the black hole metric function in the KR-PFDM spacetime background with parameters $\tau$ and $\zeta$. The Schwarzschild black hole metric is depicted by the black curve. Fixing $M = \frac{1}{2}$, we set $\zeta=0.3$ to investigate the metric function variation for different values of $\tau$ (left panel), and set $\tau = 0.06$ to research the metric function variation for different values of $\zeta$ (right panel).
• Figure 2: The variation of the event horizon as a function of parameters $\tau$ and $\zeta$ in the KR-PFDM spacetime background. For fixed $M = \frac{1}{2}$ , the variation of the event horizon with $\tau$ for different values of $\zeta$ is shown (right panel), and the variation with $\zeta$ for different values of $\tau$ is shown (left panel).
• Figure 3: For the cases of $\tau=-0.12$ (left panel) and $\tau=0.05$ (right panel), this paper presents the distribution of the Schwarzschild deviation parameter $\sigma$ as a function of $\zeta$.The white regions in the figure indicate that within these parameter ranges, our black hole model is consistent with the EHT observations at the 1$\sigma$ confidence level.
• Figure 4: Displayed is the variation of the effective potential with the tortoise coordinate under scalar field (left), electromagnetic field (middle), and gravitational field (right) perturbations for the black hole in the KR-PFDM spacetime. The parameters $M = 1/2$, $l=2$, and $\tau = -0.1$ are adopted, and the variation of the effective potential to different $\zeta$ values is analyzed.
• Figure 5: Displayed is the variation of the effective potential with the tortoise coordinate under scalar field (left), electromagnetic field (middle), and gravitational field (right) perturbations for the black hole in the KR-PFDM spacetime. The parameters $M = 1/2$, $l=2$, and $\tau = -0.1$ are adopted, and the variation of the effective potential to different $\tau$ values is analyzed.