Roy Kerr and the spin on black holes

In 1963 the New Zealand mathematician Roy Kerr achieved something that had eluded scientists for 47 years - he found the solution of Einstein's equations which describes the space outside a rotating star or black hole. Kerr's solution has been described as "the most important exact solution to any equation in physics".

Shortly after Einstein wrote down his gravitational field equations in 1915, Karl Schwarzschild found a solution which describes a non-rotating spherical star or black hole. However, it is known that all stars rotate, and that Schwarzschild's solution is at best an approximation. Kerr's achievement of finding an exact solution for the rotating case - something many had doubted could be done - was therefore a revolution in astrophysics. It ushered in a decade which might be called the Golden Age of Black Hole Physics, when General Relativity saw a Renaissance.

In the words of the legendary astrophysicist S. Chandrasekhar (Nobel laureate, 1983) [1]:

"In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe. This shuddering before the beautiful, this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound."

Over the 41 years since its discovery the Kerr solution has been pivotal in deepening our understanding of astrophysics and gravitation theory. Many new effects arise in the Kerr solution - a rotating object drags space with it, in a way which would not be possible in Newton's theory.

In recent years a wealth of new astronomical observations has provided strong evidence for the existence of rotating Kerr black holes. Most impressively, it has recently been shown from observations of matter falling into the supermassive black hole in the centre of our own galaxy that it must be rotating at close to half of the maximum rate allowed by the Kerr solution [2].

Roy Kerr's contributions have been recognised by the award of the Hughes Medal (1984) of the Royal Society, and the Hector Medal (1982) and the Rutherford Medal (1993) of the Royal Society of New Zealand.


  1. S. Chandrasekhar, "Shakespeare, Newton, and Beethoven", Ryerson Lecture, University of Chicago, 1975; reprinted in S. Chandrasekhar, "Truth and Beauty", (University of Chicago Press, 1987)
  2. R. Genzel et al., Nature 425 (2003) 934; see also

Stephen Hawking on the Kerr solution

[Excerpt from A Brief History of Time (Bantam Books, 1988), chapter 6]:

"In 1963, Roy Kerr, a New Zealander, found a set of solutions of the equations of general relativity that described rotating black holes. These "Kerr" black holes rotate at a constant rate, their size and shape depending only on their mass and rate of rotation. If the rotation is zero, the black hole is perfectly round and the solution is identical to the Schwarzschild solution. If the rotation is non-zero, the black hole bulges outward near its equator (just as the earth or the sun bulge due to their rotation), and the faster it rotates, the more it bulges. So, to extend Israel's result to include rotating bodies, it was conjectured that any rotating body that collapsed to form a black hole would eventually settle down to a stationary state described by the Kerr solution. In 1970 a colleague and fellow research student of mine at Cambridge, Brandon Carter, took the first step toward proving this conjecture. He showed that, provided a stationary rotating black hole had an axis of symmetry, like a spinning top, its size and shape would depend only on its mass and rate of rotation. Then, in 1971, I proved that any stationary rotating black hole would indeed have such an axis of symmetry. Finally, in 1973, David Robinson at Kings College, London, used Carter's and my results to show that the conjecture had been correct: such a black hole had indeed to be the Kerr solution."

A few web resources on the Kerr solution