In view of the current vogue for higher dimensional analogues - of doubtful relevance to reality - the unquestionable physical importance of Kerr's original 4-dimensional metric needs to be reiterated.
What Kerr originally sought was an asymptotically flat Einstein metric with type D Weyl tensor, but what he found turned out to be a solution also for other interesting problems, characterised by alternative local conditions: as well as the Kerr-Schild ansatz, these include a succession of progressively more sophisticated separability properties that are interpretable in terms of the presence of a Killing-Yano tensor.
However, what made the Kerr metric so important is the global property of being a solution - and indeed (as subsequent work has by now fairly rigorously established) the most general solution - of the equilibrium problem for an isolated uncharged black hole. Much modern astrophysical work is based on the presumption that Kerr's solution really does apply to what are prudently describable as "black hole candidates", but there is still no firm observational evidence for what, if confirmed, would finally establish that the validity of Einstein's theory is not restricted to the weak field regime.
BIOGRAPHICAL: Brandon Carter is Professor at the CNRS, Observatoire de Paris-Meudon, Université de Paris. He obtained his Ph.D. at the University of Cambridge in 1968, and was subsequently a Postdoctoral Research Fellow at its Institute of Astronomy 1968-1972 and then Lecturer at DAMTP, 1972-1975. In 1975 he moved from Cambridge to Paris to take up a post at Meudon, where he is currently Directeur de Recherches, Laboratoire de l'Univers Théorique. He is a Fellow of the Royal Society.
Brandon Carter is widely known for his numerous significant contributions to general relativity and relativistic astrophysics, including in particular seminal contributions on the Kerr spacetime. In 1968 he identified the "Carter constant" in geodesic motion on the Kerr geometry, and did much to elucidate the global structure of the solutions. In 1972, with Jim Bardeen and Stephen Hawking, he first proposed the laws of black hole mechanics in analogy to the laws of thermodynamics. Among other achievements he is responsible for the Carter-Penrose conformal diagrams now used as a standard tool by relativists, and in 1973 he was the first to propose the Anthropic Principle.