In this talk, I will discuss the effects of magnetic and gravitomagnetic fields in some astrophysical contexts. Considering an uniform magnetic field in the Minkowski background, I will first discuss how the propagation of gravitational wave (GW) and GW bursts are affected by the magnetic field. This formulation may be extended for non-uniform magnetic fields and in curved background, e.g, Kerr spacetime. The Kerr spacetime basically contains the mass and the Kerr parameter which is responsible for the frame-dragging effect. This is also known as the gravitomagnetic effect for the close analogy between general relativity and electromagnetic theory. Interestingly, the gravitomagnetic effect also arises in the ‘non-rotating’ Taub-NUT spacetime due to the sole presence of ‘gravitomagnetic monopole’ or NUT charge. However, the Event Horizon Telescope (EHT) has recently mapped the central compact radio source (M87*) of the elliptical galaxy M87 and shown that it is consistent with a Kerr black hole, yet alternatives to this are not ruled out. In the second part of my talk, I will discuss the possibility for the existence of NUT charge or gravitomagnetic monopole in M87* by using the results obtained from its first EHT image.