Roy Kerr, the New Zealander whose equation describes every spinning black hole in the universe

In Dallas, on 17 December 1963, three weeks after Kennedy was shot a few blocks away, a 29-year-old New Zealand mathematician named Roy Kerr was given ten minutes to present his work at the First Texas Symposium on Relativistic Astrophysics. The audience, three hundred strong, had come to hear about quasars. According to Kip Thorne’s account in Black Holes and Time Warps, many slipped out when Kerr stood up. Others read newspapers or argued in whispers. Many of the rest catnapped. The Greek-French relativist Achille Papapetrou, who had spent thirty years trying to do what Kerr had just done, stood up afterwards and admonished the audience. They half-listened to him too.

The equation Kerr presented in those ten minutes describes every spinning black hole in the observable universe. It underpins LIGO’s gravitational-wave detections since 2015. It underpins the Event Horizon Telescope’s silhouettes of M87 and Sagittarius A*. By the central theorem of stationary black-hole physics, every astrophysical black hole anywhere has the geometry Kerr wrote down at the University of Texas at Austin in late 1962 and early 1963.

He is still alive. He turns 92 on 16 May. He lives in Christchurch with his second wife Margaret. They have nine children, twelve grandchildren, and three young cats. He plays bridge well enough to have represented New Zealand internationally in the mid-1970s. In December 2023, aged 89, he posted a paper to the arXiv arguing that Roger Penrose’s 1965 singularity theorem does not prove what physicists believe it proves.

This is who he is, what he did, and where the country has been peculiarly slow to catch up.

Roy Patrick Kerr was born on 16 May 1934 at Kurow, on the south side of the Waitaki River in North Otago. His mother left the family when he was three, after his father’s infidelities. With his father at the war, Roy was sent to live on a farm. The family later moved to Christchurch, where his father ran a small rubber-band business. Roy has said he developed his counting skills there.

The household was, in his own description, dysfunctional. He told the NZ Herald in 2024 that he did not work at school. He read a great deal of books.

He was sent to St Andrew’s College, the independent boys’ boarding school in Papanui, on the strength of his father’s connection to a former headmaster. The school had no mathematics teacher during his time there. The masters identified his ability anyway. In 1950, sixteen years old, he sat the University Entrance Scholarship mathematics examinations. By his own account he turned up at the wrong session for one of the papers — the afternoon sitting of an exam that had been held in the morning — and lost the marks. He scored 298 out of 600 on the rest, won a Junior University Scholarship, and was offered a place at Canterbury University College.

He arrived in 1951. The college regulations did not let him sit first-year mathematics, so he was placed straight into third-year work. The mathematician who shaped him was the British relativity lecturer Walter Warwick Sawyer. Sawyer, watching him box as a light-welterweight in the university gymnasium, told him he did not want the best brain he had encountered in a student scrambled by a well-thrown punch. The boxing stopped. Billiards and bridge did not.

Kerr completed his BSc in 1954 and his MSc with Honours in 1955. He won a Cambridge scholarship before he had quite turned 21 — too young, by Cambridge regulation, to take it up. There were two years to fill. He spent them, on his own account, playing snooker and bridge. He briefly took up boxing again until a tutor dissuaded him.

Kerr matriculated at Trinity College, Cambridge, in September 1955. The supervisor he was assigned was a particle physicist with no interest in general relativity. The friend who pulled him into relativity was John Moffat. The seminar that made the field intelligible to him was given at King’s College London by the Italian relativist Felix Pirani in 1957.

His PhD thesis, Equations of Motion in General Relativity, was submitted in 1958 and published in three parts in Il Nuovo Cimento in 1959. The work extended what Einstein, Infeld and Hoffmann had done in the late 1930s on the motion of particles in general relativity. It was respectable. It was not what made him famous.

Kerr left Cambridge in 1958 for a postdoctoral fellowship at Syracuse University under Peter Bergmann, who had been Einstein’s collaborator at the Institute for Advanced Study. From Syracuse he moved to the Aeronautical Research Laboratory — later renamed Aerospace Research Laboratories — at Wright-Patterson Air Force Base in Dayton, Ohio. He joined the small general-relativity group run by Joshua Goldberg.

The reason a US Air Force base in Ohio had a general-relativity group is one of the small jokes of mid-century American physics, which Kerr has retold ever since: the Office of Naval Research had been funding fundamental physics for years, and the Air Force established its own pure-research programme primarily to demonstrate to the Navy that it too could.

The Wright-Patterson period mattered. In 1962, Goldberg and Rainer Sachs published the Goldberg–Sachs theorem — a result about the geometric structure of solutions to Einstein’s equations whose null geodesics behaved in a particular way. The theorem made certain classes of solutions, the ones the Russian physicist Aleksei Petrov had classified in 1954 as algebraically special, navigable in a way they had not been before.

In summer 1962, at a conference in Santa Barbara, Kerr met Alfred Schild. Schild was an Austrian-born American mathematician who had recently been given the funding by the Texas state legislature to set up the Center for Relativity at the University of Texas at Austin. He invited Kerr to join the group as a visiting member for 1962–63. Kerr arrived in Austin in late summer 1962. He went to work on the rotating-black-hole problem.

In 1916, two months after Einstein wrote down the field equations of general relativity, the German physicist Karl Schwarzschild — serving on the Eastern Front — sent Einstein an exact solution describing the spacetime around a non-rotating spherical mass. Schwarzschild died of a skin disease contracted at the front a few months later. The Schwarzschild solution remained the only known stationary vacuum exact solution to Einstein’s equations for nearly half a century.

But every astrophysical mass rotates. The Schwarzschild solution was, on rotation grounds, the wrong solution for almost every real object in the universe. Hermann Weyl had tried for the rotating case. Hans Reissner and Gunnar Nordström had tried for a charged version. Achille Papapetrou had spent thirty years trying. The reason was the difficulty of the equations: Einstein’s field equations are ten coupled non-linear partial differential equations in four variables, and exact solutions arise only in cases of high symmetry. Stationary axisymmetric spacetimes have less symmetry than spherically symmetric ones. The equations resist them.

Kerr’s mathematical move, when he looked at the problem in late 1962, was indirect. Rather than trying to solve Einstein’s equations head-on for a rotating mass, he asked which solutions were algebraically special in the Petrov sense. The Goldberg–Sachs theorem then converted the problem into a problem about congruences of null geodesics with the right geometric properties.

Working in the Newman–Penrose null-tetrad formalism that Ezra Newman and Roger Penrose had introduced in 1962, Kerr could write Einstein’s equations as a system of first-order equations on a complex two-form. In early 1963 a Newman–Penrose preprint appeared to prove that the kind of solution he was trying to find could not exist. He read it carefully and found a gap. The proof had assumed something that was not warranted. Within a few weeks of finding the gap, he had the metric.

The paper was a page and a bit. It was titled Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics. It appeared in Physical Review Letters on 1 September 1963. It gave the metric in Kerr’s original coordinates — coordinates almost entirely supplanted, since 1967, by the Boyer–Lindquist coordinates. It gave the parameters: mass M and angular momentum per unit mass a. It noted that for a = 0 the metric reduced to Schwarzschild’s. It did not work out the maximum analytic extension or the global structure. Those came later.

The metric encodes every property of a rotating black hole — frame dragging, the ergosphere, the inner Cauchy horizon, the ring singularity at the centre — in an off-diagonal dt dφ term that is the technical signature of the rotation. It is what tells you that the time direction and the angular direction have been mixed by the spinning mass.

Kerr has consistently said in interviews that the discovery was not inspiration. The mathematical machinery had become available in 1962. Someone was going to do it. He has said, more than once, that if he had not done it, somebody else would have within five or ten years. The fact that nobody had done it for forty-seven years was an accident of who had looked at the problem, and how.

The First Texas Symposium ran 16–18 December 1963 at the Adolphus Hotel in Dallas, three weeks after Kennedy was shot a few blocks away. Three hundred physicists and astronomers came, most of them to hear about quasars. Maarten Schmidt’s redshift result on 3C 273 had appeared earlier that year and had made quasars the unsolved problem of the moment.

Kerr was given a ten-minute slot on the second-to-last day. The original organisers had intended to have Penrose present the work — Penrose was the better speaker — and Kerr had objected strongly. He gave the talk himself.

Kip Thorne, in Black Holes and Time Warps, describes the scene: many slipped out when Kerr stood up; others, less polite, argued in whispers; many of the rest catnapped. Papapetrou stood up afterwards and told the audience that what they had just heard was the answer to the problem he had failed to solve in three decades. The room half-listened.

Cygnus X-1, the first stellar-mass black hole candidate, was identified eight years later. The supermassive black hole models of quasar power that became standard by the late 1960s used the Kerr metric. The audience that came to Dallas to hear about quasars had been, in those ten minutes, told what quasars were.

In 1965 and 1966, working at the University of Texas at Austin, the British mathematician Robert Boyer extended Kerr’s work in two important ways. With Richard Lindquist, he constructed the maximum analytic extension of the Kerr metric — the global structure of the spacetime, including the inner horizon, the Cauchy horizon, and the ring singularity. The coordinate system in which the modern Kerr metric is almost universally written, the Boyer–Lindquist coordinates, came from this work. The paper that introduced them, Maximal Analytic Extension of the Kerr Metric, was published in the Journal of Mathematical Physics in 1967.

Boyer never saw it. On 1 August 1966, Charles Whitman, a 25-year-old former Marine, climbed to the observation deck of the Main Building tower at the University of Texas with a footlocker of weapons. Over the next ninety minutes he killed sixteen people and wounded thirty-one before being shot dead by Austin police. Boyer was on his way to lunch when he was killed. The 1967 paper introducing Boyer–Lindquist coordinates was published posthumously.

The late 1960s and 1970s were when the Kerr metric stopped being an exact solution and became the description of every astrophysical black hole.

Roger Penrose’s 1965 singularity theorem established that, under reasonable physical assumptions, gravitational collapse generically produces singularities — that black holes are not pathological cases but inevitable.

Werner Israel proved in 1967 that any static vacuum black hole in general relativity must be Schwarzschild’s. Brandon Carter, working at Cambridge, extended the result in 1971 to axisymmetric vacuum solutions, showing that any stationary, axisymmetric vacuum black hole with a regular event horizon must be Kerr’s. Stephen Hawking strengthened the assumptions in 1972. David Robinson completed the rotating-vacuum case in 1975. Pawel Mazur completed the charged case (the Kerr–Newman metric) in 1982.

The combined theorem — the no-hair theorem — says that any astrophysical black hole, given enough time to settle, must be described by the Kerr metric, characterised entirely by its mass and its angular momentum. Two parameters. The shape of the star that collapsed, its chemistry, its magnetic fields, its angular momentum distribution, its irregularities — all radiated away in gravitational waves during the settling-down. What remains is Kerr.

In 1965, with Ezra Newman of the University of Pittsburgh, the metric was extended to include electric charge. The Kerr–Newman metric was discovered, in Newman’s own description, “by guesswork”: he and his collaborators wrote down the obvious generalisation, plugged it into Einstein–Maxwell, and it worked. Kerr was not a co-author on the Kerr–Newman paper, despite the eponym.

The Kerr–Schild metrics, on the other hand, are work he did with Schild. Their 1965 paper, Some algebraically degenerate solutions of Einstein’s gravitational field equations, introduced a class of solutions to Einstein’s equations of which Kerr’s is the most famous example.

In 1971, after nearly a decade in Texas, Kerr returned to New Zealand. The University of Canterbury offered him the Chair of Mathematics. He took it. He turned down posts at major American and European universities to do it.

He directed the Mathematics Department at Canterbury from 1983 to 1993. The colleagues who served under him, quoted in the NZ Mathematical Society Newsletter on his retirement, described his leadership as “at once uncompromising and dashing”. He fought to reduce the student-to-staff ratio. He pushed the department toward research. He brought in computers against older colleagues’ resistance. He retired from Canterbury in 1993.

He played bridge through these years. He represented New Zealand internationally in the mid-1970s. He co-developed the Symmetric Relay System, a contract-bridge bidding system still in occasional tournament use.

The Hector Memorial Medal of the Royal Society of New Zealand in 1982. The Hughes Medal of the Royal Society of London in 1984. The Rutherford Medal of the Royal Society of New Zealand in 1993, the inaugural year of that name. The Marcel Grossmann Award of ICRANet in 2006. Appointment to the Yevgeny Lifshitz Chair at ICRANet in Pescara, Italy, in 2008. The Companion of the New Zealand Order of Merit in 2011. The Albert Einstein Medal of the Albert Einstein Society in Bern in 2013, the first New Zealander to receive it.

In 2016 he shared the Crafoord Prize in Astronomy with Roger Blandford of Stanford. The Crafoord Prize is the prize the Royal Swedish Academy of Sciences awards in disciplines the Nobel does not cover. The 2016 prize was 6 million Swedish kronor, divided equally — about NZ$1 million each. The citation was for fundamental work concerning rotating black holes and their astrophysical consequences.

Election as a Fellow of the Royal Society of London followed in 2019. The Oskar Klein Medal of Stockholm University in 2020. The ICTP Dirac Medal in 2025, jointly with Gary Gibbons, Gary Horowitz and Robert Wald. Kerr was 91.

Subrahmanyan Chandrasekhar, Nobel laureate in physics in 1983, devoted his great late book The Mathematical Theory of Black Holes (1983) to a systematic exposition of the Kerr metric. The line everyone quotes is from his Ryerson Lecture at the University of Chicago in 1975:

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.

Stephen Hawking, in A Brief History of Time, gave Kerr’s solution a single sentence: In 1963, Roy Kerr, a New Zealander, found a set of solutions of the equations of general relativity that described rotating black holes.

At 09:50:45 Universal Time on 14 September 2015, two months before the LIGO instruments at Hanford and Livingston were officially open, a pair of black holes — one of about 36 solar masses, the other of about 29 — collided 1.3 billion light years away. The resulting gravitational wave passed through both detectors within seven milliseconds of each other. The waveform, a chirp lasting 0.2 seconds, was decoded over the following months. The merger had produced a final black hole of about 62 solar masses, with about 3 solar masses of energy radiated as gravitational waves in the final fraction of a second.

The interpretation of GW150914 — and of every binary black-hole merger LIGO and Virgo have detected since — is built on the Kerr metric. The inspiral phase is computed using post-Newtonian expansions around two Kerr objects orbiting each other. The merger phase uses numerical relativity codes that solve Einstein’s equations directly with the Kerr metric as background. The ringdown phase, the final fifty milliseconds, is dominated by the quasinormal modes of the Kerr black hole — frequencies that are characteristic of Kerr in the way the resonant frequencies of a bell are characteristic of the bell.

When LIGO announced GW150914 on 11 February 2016, the no-hair theorem was, for the first time, observationally tested. The ringdown frequencies were, within the precision of the measurement, the Kerr quasinormal frequencies. The University of Canterbury sent out a press release. Kerr told the NZ Herald he was pleased.

In April 2019 the Event Horizon Telescope released the first image of a black hole’s silhouette — the supermassive object at the centre of the elliptical galaxy M87, fifty-five million light years away. The shadow’s size, asymmetry and angular structure all matched the Kerr predictions. In May 2022 the EHT released the corresponding image of Sagittarius A*, the supermassive black hole at the centre of the Milky Way. Same result.

Kerr was 85 for M87 and 88 for Sagittarius A*. He watched the announcements live. His public response, both times, was that he had assumed the universe was doing what it was doing. The interesting thing was that the human race had finally built the instruments to look.

In December 2023 Kerr posted a single-author paper to the arXiv, titled Do Black Holes have Singularities? (arXiv:2312.00841). He was 89.

The paper argues that Penrose’s 1965 singularity theorem proves something less than what physicists believe it proves. Penrose’s theorem establishes the existence of finite-affine-length light rays — null geodesics that, in a generic black-hole spacetime, terminate after finite affine parameter at points that cannot be extended. The standard interpretation, taught for fifty years, is that these light rays end at singularities — points of infinite curvature where general relativity breaks down.

Kerr’s argument is that this interpretation slips an assumption past the reader. The theorem proves the rays terminate. It does not prove that what they terminate at is a curvature singularity. He produces, in the Kerr metric, examples of null geodesics that asymptote to an event horizon without terminating at any singularity. He concludes that the assumption equating finite affine length with curvature singularity is “dodgy” — his word — and that Penrose and Hawking did not prove what they thought they had proved.

Reception has been split. Sabine Hossenfelder, on her widely-followed YouTube channel, defended the substance of Kerr’s argument and noted that the elision he points to is real in textbook treatments. Ethan Siegel, writing in Big Think, took the paper seriously enough to walk through it for a general audience. Other physicists have argued that Kerr is using a non-standard definition of “singularity” and is rebutting a claim that working relativists do not actually make in the technically careful form. The argument is unresolved.

Kerr’s first wife was Joyce. They married in the late 1950s. Their daughter Susan was born microcephalic after Joyce was X-rayed at the US Embassy in London for an American visa without knowing she was pregnant. Susan died at the age of seven.

He married Margaret in the 1960s. They have nine children and around twelve grandchildren. Margaret bred golden retrievers for years; the household at one point contained twenty-one of them. The retrievers gave way to cats. The current household holds three.

The Kerrs lived in Tauranga for nine years before moving back to Christchurch in 2022. He still works. The principal recreations are Sudoku, bridge, the cats, and the company of the children and grandchildren.

The lines from his interviews are characteristic. On schoolwork: I didn’t do any work, but I did read a hell of a lot of books. On marriage: Do what you’re told. But I don’t always. On his own intellectual style: If there’s been anything in my life that I’ve been good at, it’s picking out rubbish.

Before September 1963, general relativity had a single exact stationary vacuum solution, Schwarzschild’s. It described non-rotating spherical masses. The geometry of rotating gravity had been an open problem for forty-seven years.

After September 1963, every rotating mass had an exact stationary vacuum description: Kerr’s. The metric had two parameters, mass M and angular momentum aM. It reduced to Schwarzschild when a equalled zero. It had an event horizon at one radius and an inner horizon at a smaller one. Between the event horizon and an outer surface, the static limit, lay a region called the ergosphere, inside which spacetime was being dragged along by the rotation of the mass so vigorously that no observer could remain stationary relative to a distant inertial frame. Particles in the ergosphere were forced to orbit the central mass in the direction of rotation. This is frame dragging — the most distinctively rotational feature of the metric, and the feature whose first direct measurement, by Gravity Probe B in 2011, took half a century of instrumentation to achieve.

Beyond the ergosphere lay the central exotic structure. The Schwarzschild solution’s singularity is a point at the centre of a spherical horizon. Kerr’s is a ring in the equatorial plane. The ring sits inside an inner horizon that is itself inside the event horizon. The interior of the inner horizon — the Cauchy horizon — has the property that an observer falling through it loses the ability to predict the future from the past, because the spacetime has closed timelike curves near the ring. The geometry, in the strict mathematical sense, allows time travel. Whether anything physical can take advantage of this — whether the inner horizon is stable to perturbations, whether the ring singularity is generic in real collapse, whether the closed timelike curves are merely artefacts of the idealised exact solution — has been one of the recurring research questions in black-hole theory since the early 1970s.

The whole machinery of modern black-hole physics — Penrose processes by which energy can be extracted from rotating black holes by exploiting the ergosphere, superradiant scattering of waves off rotating horizons, the Blandford–Znajek mechanism for powering quasar jets from the rotational energy of supermassive black holes, the Bardeen–Press–Teukolsky analysis of perturbations of rotating black holes — depends on Kerr’s metric as the underlying geometry. Without it, none of these results exist. The discipline has, since 1963, been a Kerr-metric discipline.

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He has produced one equation. The equation describes most of the gravitational structure of the universe. He has done it from Christchurch, with a thirteen-year detour through Cambridge, Syracuse, Wright-Patterson and Texas. He has not been a public figure in the New Zealand sense Hillary or Rutherford were.

He turns 92 on 16 May. He is in Christchurch with Margaret. He is reading. He is doing Sudoku. He is occasionally writing a paper that picks a fight with the orthodoxy of his field, sixty years after his original orthodoxy-overturning intervention. He has not stopped looking carefully at the rubbish.

Sources and further reading

• Roy Kerr, “Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics,” Physical Review Letters 11(5): 237–238 (1 September 1963)
• Kip Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy (Norton, 1994)
• Fulvio Melia, Cracking the Einstein Code: Relativity and the Birth of Black Hole Physics (University of Chicago Press, 2009) — with an afterword by Kerr
• S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford University Press, 1983)
• MacTutor — Roy Kerr biography
• University of Canterbury — notable alumni: Roy Kerr
• Royal Society — Roy Kerr
• Crafoord Prize 2016 announcement
• R. P. Kerr, “Do Black Holes have Singularities?” arXiv:2312.00841 (December 2023)
• NZ Herald, “Roy Kerr turns 90: Inside the beautiful mind of a Kiwi genius” (May 2024)
• John McCrone, The Press, “Bright sparks and black holes” (2 March 2013)

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