Kretschmann Scalar for a Kerr-Newman Black Hole

Kretschmann Scalar for a Kerr-Newman Black Hole

Henry, Richard Conn
The Astrophysical Journal 535, no. 1 (2000): 350
https://doi.org/10.1086/308819

“Black holes have been invoked in astrophysics to account for some galactic X-ray sources, and also for the engines that drive active galactic nuclei. Physicists, however, have provided no way to visualize any realistic black hole. This paper remedies all of that. A scalar is derived that characterizes the spacetime curvature of a realistic rotating black hole, allowing one to “see” the black hole. Once in possession of the algebraic expression for the curvature, which is called the Kretschmann scalar, any possible black hole can be visualized realistically. My derivation includes the possibility of electric charge on the black hole, although real black holes in the universe are very likely to be neutral. I include the possibility of electric charge simply to ensure that all possible black holes are covered in my analysis.”

— Richard Conn Henry