Shadow and weak gravitational lensing of RN-like BH in plasma

In this paper, we investigate weak gravitational lensing and shadow radius in the Kalb–Ramond (KR) gravity for an Reissner–Nordström-like (RN-like) black hole (BH). The examination is carried out in three distinct frameworks: uniform plasma, singular isothermal sphere(SIS), and non-singular isothermal sphere (NSIS). When a gravitating object is surrounded by plasma, the lensing angle is determined by the frequency of the electromagnetic wave, plasma dispersion, plasma inhomogeneity, and gravity. Even in uniform plasma, the gravitational photon deflection angle differs from that in a vacuum and depends on photon frequency due to the second effect. We consider both effects and calculate the lensing angle for a significantly non-uniform plasma in the existence of KR gravity. Utilizing observational data from the Event Horizon Telescope (EHT) project for Sgr A*, we have obtained that which range of RN-like black hole’s parameters $Q$ and $l$ correspond observations as well as when the Lorentz-violating parameter $l$ rise, radius of black hole shadow decrease. To connect a relationship with observations data, we examine the magnification and positioning of images produced by lensing, as well as the weak deflection angle and magnification for sources located near various galaxies.