Stephen Hawking (1942-2018).

Autograph letter signed (‘Stephen Hawking’) to Charles W. Misner, n.p., n.d. [early 1968].

2½ pages, 203 x 253mm. Provenance: Charles W. Misner.

Hawking proposes an exciting new definition for space-time singularity. Administrative matters are dispensed with quickly and with characteristic mischievous humour, as Hawking thanks Misner for the cheque ‘which was the more welcome for coming after devaluation. I will pay £18-2-6 into your Cambridge account’ before getting to the scientific crux of the matter: ‘I want to propose a new definition of what should be regarded as a physical singularity; space-time is singularity free if and only if it is geodesically bounded. By this I mean that under the exponential map every compact set in the timeline and null region of the tangent bundle maps into a set in the manifold with compact closure’. He then goes on to illustrate his meaning, ‘geodesically complete => geodesically bounded => distant boundaries’, noting that the ‘arrows in the reverse direction hold if the strong causality condition holds. I can show that is there is a compact slice with converging normals and if the density is not zero at some point of the slice then space-time is not geodesically bounded’. He thanks Misner for aChristmas card: 'I hope the one we sent you of Robert did not get lost in the New York postal fire'.

Stephen Hawking first published on singularity theorems in his 1965 Cambridge doctoral thesis, his approach to studying the implications and consequences of the expansion of the universe inspired by the work of Roger Penrose on black holes. The next year, Hawking and Penrose shared the 1966 Adams Prize – Hawking’s winning essay was entitled ‘Singularities and the Geometry of Space-Time’ – and the two men began to work collaboratively on the set of concepts now known as ‘Penrose–Hawking singularity theorems’, which had at their centre the notion of geodesical incompleteness mentioned here by Hawking. Penrose and Hawking shared their field with the American physicist Charles W. Misner, who was working on geodesical incompleteness at the University of Maryland; Misner had called for more clarity in the concept of space-time singularity in a 1963 paper in the Journal of Mathematical Physics. Hawking and Misner first met during the latter’s 1966-67 visit to Cambridge at the invitation of Hawking’s postgraduate supervisor Dennis Sciama – the two colleagues became close, and Hawking asked Misner to act as godfather to his son, Robert, who was born in May 1967.

Sold to create an endowment in the College of Computer, Mathematical, and Natural Sciences at the University of Maryland, College Park, in remembrance of the early contributions of the Department of Physics at the University of Maryland, and particularly of Joseph Weber, to the advent of Gravitational Wave Astronomy.

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