Nearly Static Magnetized Kerr Black-hole in Non-linear Electrodynamics

We have analyzed the thermodynamics of slowly rotating magnetized Kerr black-hole, with typical spin parameter $a\le 0.1$ (nearly static) in the background of non-linear electrodynamics. In particular we have studied the Bekenstein-Hawking entropy, Hawking temperature, angular momentum, specific heats and identified regions of parameters for possible phase-transitions. It turns out that once the stability lost the black-hole never come back to its original stable position.