Study of tunneling radiation and thermal fluctuations of a gauge super gravity like black hole

Abstract: The Newman-Janis technique and the semi-classical Hamilton-Jacobi approach are two distinct phenomena that we apply in this paper to examine the Hawking temperature $(T_{H})$ for $4$-dimensional gauge super gravity like black hole with rotation parameters. First, using the Newman-Janis algorithmic approach, we compute the gauge super gravity like black holes solution. We use surface gravity to derive the $T_H$ for a gauge super gravity like black hole. In order to do this, we use the Lagrangian field equation in the background of generalized uncertainty principle, semi-classical Hamilton-Jacobi approach and the WKB approximation technique. Furthermore, we investigate the stability of considered geometry with the help of corrected entropy and well known thermodynamic quantities. It is concluded that the gauge super gravity like black holes is stable under first-order corrections.