Shadow of slowly rotating Kalb-Ramond black holes

Real astronomical objects possess spin, yet deriving exact solutions for rotating black holes within gravitational theories is a formidable challenge. To understand the shadow of rotating black holes in Lorentz-violating spacetimes induced by antisymmetric tensor fields, known as Kalb-Ramond (KR) fields, we have focused on the slow-rotation approximation framework. Using this approach, we have obtained first-order rotation series solutions, which describe slowly rotating KR black holes. For this solutions, we have plotted the black hole shadow contours under various parameters using the numerical backward ray-tracing method. As the Lorentz-violating parameter increases, not only the apparent size of the black hole shadow decreases, but also the effects of rotation, such as the D-shaped structure and frame-dragging, are amplified. Furthermore, the KR field also enhances gravitational lensing, causing the shadow to occupy a larger area within the photon ring. This distinctive feature can differentiate KR gravity from general relativity. Additionally, using the latest observational data from EHT on M87* and Sgr A*, we have provided constraints on the Lorentz-violating parameter of rotating KR black holes. We found that, compared to static black holes, rotating black holes allow for the presence of stronger Lorentz violation effects.