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We present firstly the equation of motion for a test scalar particle couplingto Einstein tensor in the Schwarzschild-Melvin black hole spacetime through theshort-wave approximation. Through analysing Poincar\'{e} sections, the powerspectrum, the fast Lyapunov exponent indicator and the bifurcation diagram, weinvestigate the effects of coupling parameter on the chaotic behavior of theparticles. With the increase of the coupling strength, we find that the motionof coupled particle for the chosen parameters becomes more regular and orderfor the negative couple constant. While, for the positive one, the motion ofcoupled particles first undergoes a series of transitions between chaoticmotion and regular motion and then falls into horizon or escapes to spatialinfinite. Our results show that the coupling brings about richer effects forthe motion of the particles.

Chaos in the motion of a test scalar particle coupling to Einstein tensor in Schwarzschild-Melvin black hole spacetime