Black hole with global monopole charge in self-interacting Kalb-Ramond field

In this study, we explore a static, spherically symmetric black hole solution in the context of a self-interacting Kalb-Ramond field coupled with a global monopole. By incorporating the effects of Lorentz-violating term $\ell$ and the monopole charge $\eta$ in the KR field, we derive the modified gravitational field equations and analyze the resulting black hole spacetime. The obtained solution exhibits deviations from the Schwarzschild metric with topological defect, as it is influenced by the monopole charge and self-interaction potential. We investigate the thermodynamic properties of the black hole, including its Hawking temperature, entropy, and specific heat, revealing novel stability conditions. Additionally, we perform solar system tests such as perihelion precession, gravitational redshift, light deflection, and time delay of signals to impose constraints on the Lorentz-violating parameter and monopole charge. Our findings suggest that these parameters have to be significantly small, although there are different constraints imposed by individual tests, ranging from $10^{-9}\leq|\ell|\leq 10^{-4}$ and $10^{-9}\leq\eta\leq 10^{-6}\, \mathrm{m}^{-1}$.