Atticus Rare Books

Gravitational field of a spinning mass as an example of algebraically special metrics in Physical Review Letters 11 Number 5, September 1, 1963, pp. 237-238 [LANDMARK KERR BLACK HOLE PAPER SOLVING EINSTEIN’S GENERAL RELATIVITY EQUATIONS; KERR’S BLACK HOLES PROVEN STABLE IN 2022]

Kerr, Roy

New York: American Physical Society, 1963. 1st Edition. FIRST EDITION OF KERR’S LANDMARK 1963 PAPER DESCRIBING THE MATHEMATICS OF ROATATING BLACK HOLES, A WORK THAT EXACTLY SOLVED EINSTEIN’S EQUATIONS OF GENERAL RELATIVITY. Not infrequently, Kerr’s achievement is described without hyperbole as the most important exact solution to any equations in physics. “In 2022, it was mathematically demonstrated that the equilibrium found by Kerr was stable and thus black holes—which were the solution to Einstein's equation of 1915—were stable” (Wikipedia).

As said, researchers finally proved Kerr’s black holes stable in 2022. This meant, essentially, that if shaken, they settle back into a form like the one they began with. The opposite situation — a mathematical instability — would not have proved Kerr wrong, but it “would have posed a deep conundrum to theoretical physicists and would have suggested the need to modify, at some fundamental level, Einstein’s theory of gravitation” (Quanta; T. Damour, Institute of French Advanced Scientific Studies).

In a series of lectures in Berlin in 1915, Einstein introduced his theory of general relativity using equations to demonstrate that energy and matter affect the shape of space-time, causing it to curve. In the paper offered here, the New Zealand mathematician Roy Kerr achieved something that had eluded scientists for 47 years - he found the solution of Einstein's general relativity equations which describes the geometry of empty spacetime around a rotating black hole. Einstein’s field equations are highly non-linear, making finding exact solutions very difficult to find.

All prior solutions to Einstein’s general relativity equations involved static masses – non-rotating ones. Given that virtually all stars rotate, it was likely that most or all black holes also rotate. Kerr’s work provided a realistic model of a rotating star that becomes a black hole; he discovered an exact solution to Einstein’s field equations (now called the Kerr Metric).

“A Kerr black hole does not collapse to a point, but instead into aspinning ring of neutrons. The ring is circulating so rapidly (because of the conservation of angular momentum) that centrifugal force keeps the black hole from completely collapsing under gravity, avoiding a singularity. Kerr black holes have a second horizon outside the event horizon, a flattened sphere now called the “ergosphere” within which everything, including light, is caused to rotate by the curvature of spacetime” (Wenner Collection).

The Nobel Laureate Subrahmanyan Chandrasekhar wrote about the importance of Kerr’s achievement, saying “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” (Chadrasekhar, Truth and Beauty: Aesthetics and Motivations in Science).

Kerr's achievement in finding an exact solution for the rotating case, for Einstein’s equations of General Relativity, was something many doubted could be done; it was a revolution in astrophysics. It certainly ushered in one. Item #1641

CONDITION & DETAILS: New York: American Physical Society. Volume 11, July to December 1963. Full volume. Ex-libris with only a blind stamp to the rear ffp. and a discreet (see photo) stamp at foot of spine. 4to (10.5 x 8 inches; 263 x 200mm). [4], pp. 576, [2]. Bound in green buckram showing only very slight wear. The interior is pristine. Near fine.

Price: $600.00