Rotating black hole in an external electromagnetic field

The electromagnetized Kerr metric is used to provide a model for the exterior spacetime of a rotating black hole immersed in an external electromagnetic field. As compared to the vacuum Kerr metric, the electromagnetic field neither changes the location nor the proper area of the event horizon. However, it pulls in the static limit. Further, for a suitable value of the electromagnetic field, no ergosphere can be formed. An algorithm is developed to analyze, using algebraic computing, the equatorial circular timelike and null geodesics. As an application, we study the test-particle motion around a supermassive rotating black hole immersed in a strong electromagnetic field. It is shown that the electromagnetic field enhances the test-particle release of energy, although it diminishes the probabilities of extraction of energy through the Penrose process.