Rotating black hole shadows in metric-affine bumblebee gravity

Abstract

In this work, we investigate the structure of black hole shadows in the bumblebee gravity model formulated within the metric-affine framework, which incorporates spontaneous Lorentz symmetry breaking (LSB) through a vector field $B_μ$ with a non-zero vacuum expectation value. We analyze the influence of the dimensionless rotation parameter $a = J/M$ and the Lorentz-violating (LV) coefficient $X = ξb^2$ on the photon sphere radius, the critical impact parameter, and the shadow morphology. Using ray-tracing simulations with the GYOTO code and accretion disks, we observe that increasing values of $X$ induce progressive vertical flattening, asymmetric ``teardrop''-shaped deformations, and local collapse of the lower silhouette region, interacting with the rotational Doppler effect. These anisotropic signatures distinguish the bumblebee model from the standard Kerr metric and provide observational tests for LV effects in strong gravity regimes, potentially detectable by the Event Horizon Telescope in sources such as M87* and Sgr A*.

Figures (12)

• Figure 1: The figure represents the intensity profile in relation to the shadow, with the rotation parameter "a" varying, without interference from the LV parameter, thus $X=0$. In figure (a) we have $a = 0$, (b) we have $a = 0.3$, (c) we have $a = 0.6$, and (d) we have $a = 0.9$.
• Figure 2: The figure represents the intensity profile in relation to the shadow, with the rotation parameter $a$ varying and the LSB parameter fixed ($X$). In the first row (a), we have $X=0.2$. In the second row (b), $X=0.5$, and finally, in (c), the value is $X=0.9$, with the rotation values given by $a=0.0$, $0.3$, $0.6$, and $0.9$.
• Figure 3: The figure represents the intensity profile in relation to the shadow, with the rotation parameter $a = 0.0$ fixed and varying $X$. In figure (a) we have $X = 0.0$, (b) we have $X = 0.2$, (c) we have $X = 0.5$, and (d) we have $X = 0.9$.
• Figure 4: The figure shows the intensity profile in relation to the shadow. In the first row, the rotation parameter $a=0.6$ is fixed. In the second row, the rotation parameter $a=0.9$, where in both cases we vary the values of $X = 0.0, 0.2, 0.5,$ and $0.9$, respectively.
• Figure 5: The figure shows the behavior of the shadow with the LSB parameter fixed at $X=0$, varying the rotation parameter. In the first row, we have the Schwarzschild case. In the second row, we have the Kerr-type metric, where we increase $a$ from 0 to 0.9.