Optical phenomena in a non-commutative Kalb–Ramond black hole spacetime

This work investigates additional gravitational features of a newly proposed black hole spacetime within Kalb-Ramond gravity, incorporating non-commutative corrections arising from a gauge-theoretic approach recently introduced in the literature [arXiv:2507.17390]. Accordingly, null geodesics are solved numerically to trace photon paths; the photon sphere and shadow are determined. From Event Horizon Telescope (EHT) measurements of $Sgr A^{*}$, constraints on the parameters $Θ$ (which encapsulates the non-commutativity) and $\ell$ (the Lorentz-violating parameter) are established. To examine the stability of critical orbits and the deflection angle (gravitational lensing) in the weak field scenario, we compute the Gaussian curvature in order to use the Gauss-Bonnet theorem. Moreover, the deflection angle has been calculated as well in the strong deflection limit. Furthermore, Lensing observables are estimated using EHT data for $Sgr A^{*}$ and $M87$. Topological features such as the topological photon sphere are also explored.