  Ever since its discovery by Roy Kerr in 1963, the geometry around rotating,
electrostatically-neutral black holes, otherwise known as Kerr black holes, has
significantly contributed to theoretical developments in the fields of general
relativity, thermodynamics and beyond. Extremal Kerr black holes, in which the
spin parameter of the rotating black hole is at a maximum without breaching
certain postulates, has especially been of interest to the research community
due to its sensitivity to higher order corrections to Einstein's theory of
relativity. In this paper, we review some unresolved open questions regarding
the discontinuity of certain properties of the Kerr black hole as it approaches
the extreme limit. These include the form of the innermost stable circular
orbit (ISCO), the nature of vanishing entropy, and the disappearance of the
trapped surface as a Kerr black hole approaches extremality. We conclude that
current theories are likely not suitable for studies of extremal black holes,
and we posit that further development in theory may likely require a quantum
approach to gravity. G=c=1 and Einstein summation convention are assumed
throughout this paper.
