Spinning Black Holes: Basic Properties

Abstract

Astronomical bodies usually rotate and spinning BHs have become quite important in BH physics studies. In this chapter we introduce spinning BHs with axial symmetry about an axis (the z-axis), and with time independent (stationary) metric $g_{\mu \nu }$. We will see that rotation, in turn, introduces naturally a cross term $\text {c}\,\!\text {d}t\,\text {d}\phi$ in the line element with an obvious symmetry under simultaneous reversals of $\text {d}t \rightarrow - \text {d}t$, and $\text {d}\phi \rightarrow -\text {d}\phi$, which, in turn, describe the two possible directions of the rotation. Hence the corresponding solution is stationary but not static.