Optical Appearance and Ringdown of Black Holes in a Kalb Ramond Field Coupled to Perfect Fluid Dark Matter

Abstract

This paper investigates the optical and dynamical properties of a static spherically symmetric black hole in the presence of a Kalb--Ramond (KR) field coupled to perfect fluid dark matter (PFDM). We analyze the effects of the Lorentz-violating parameter $α$ and the dark matter parameter $λ$ on photon trajectories and their observational signatures in the strong-gravity regime. Furthermore, we study the quasinormal mode spectrum under scalar, electromagnetic, and gravitational perturbations, examining how the model parameters influence the characteristic oscillation frequencies and damping rates. In particular, the interplay between the effective potential structure and perturbative dynamics is clarified, and it is found that, within the validity of the eikonal approximation, the quasinormal modes of the black hole considered here exhibit good agreement with the properties of null geodesics. Our results show that the model parameters significantly affect both the optical appearance of the black hole and the dynamical features of the ringdown phase, providing potential observational constraints on Lorentz-violating effects and dark matter environments in strong-field regimes.

Figures (9)

• Figure 1: Plot of $G(u)$ for photon trajectories in the black hole spacetime when $\alpha = 0.05$ and $\lambda = 0.015$.
• Figure 2: Relationship between the number of photon orbits $n$ and the impact parameter $b$ in the black hole spacetime when $\alpha = 0.05$ and $\lambda = 0.015$. The right panel shows the photon trajectories in polar coordinates $(r,\phi)$ for different impact parameters.
• Figure 3: The first three transfer functions of a thin accretion disk around the black hole spacetime when $\alpha = 0.05$ and $\lambda = 0.015$.
• Figure 4: Emission intensity (first column), observed intensity (second column), and density maps (third column, with $\alpha = 0.15$) of the thin accretion disk around the black hole for different values of the Lorentz parameter $\alpha$, with $\lambda = 0.005$ fixed.
• Figure 5: Emission intensity (first column), observed intensity (second column), and density maps (third column, with $\lambda = 0.015$) of the thin accretion disk around the black hole for different values of the dark matter parameter $\lambda$, with $\alpha = 0.05$ fixed.