[Christodoulou] himself confesses today that it was his futile attempt to find the non-existent solution that caused him to suspect the immense depth of mathematics.

After one year Christodoulou entered the graduate school and started collaborating with me. At the time I was working with Wheeler on the effective potential approach to geodesics co-rotating and counter-rotating in the Kerr metric. In parallel, Frank Zerilli was working on the gravitational radiation emitted by the fall of a test particle in a Schwarzschild black hole. A new approach started with the arrival of Demetrios: he was just creating mathematics following his needs. We identified the reversible and irreversible transformations of a Kerr black hole. Wheeler advanced a thermodynamic analogy. I addressed the need of identifying the concept of irreducible mass and Demetrios's contribution was to integrate, overnight, the differential equation for infinitesimal reversible transformations which led to the finite mass-energy formula of a Kerr black hole. That evening, while walking back home through the Institute for Advanced Study woods, I expressed to Wheeler the great relevance of the newly found formula by Demetrios and proposed to let Demetrios be the single author of this article, admiring his great mathematical talent. Wheeler agreed.

When I first presented [the paper], Wheeler, seeing that a new chapter was opening, the thermodynamics of black holes, became so excited that he set off firecrackers. He had, you know, a particular love of explosions.

I would like to thank Professor J A Wheeler and Dr R Ruffini for very helpful discussions and suggestions.

A formula is derived for the mass of a black hole as a function of its "irreducible mass," its angular momentum, and its charge. It is shown that 50% of the mass of an extreme charged black hole can be converted into energy as contrasted with 29% for an extreme rotating black hole.

This thesis deals with the physics of gravitational collapse and its final states, the collapsed objects called black holes. We know that a star, that is at the end point of thermonuclear evolution, will be unstable against gravitational collapse if its mass is larger than a certain critical mass. Will radiation be similarly unstable above a certain critical mass-energy and undergo gravitational collapse? This question is treated in Chapter II, in considering an imploding and re-exploding scalar pulse of radiation, and is answered in the affirmative.

Will a black hole always be stationary? Will the physics of the dynamical region inside the event horizon never come into play? No - in Chapter III it is shown that the dynamics of the interior geometry comes into play in the final stages of collapse of the Universe itself, and the Schwarzschild singularity is amalgamated into the Friedmann singularity.

In Chapter V, we show various processes that extract energy from a rotating black hole. The first such method was investigated by R Penrose. Here, the concepts of irreducible mass and of reversible and irreversible transformations in black holes are introduced. ...

The details of the magnetic and electric field to be expected in a collapsed object nonradioactive at infinity ("Black Hole") are here given. Also given are the formulae determining the maximum total energy extractable from a collapsed object and the definition of its angular velocity as seen from infinity. Physical meaning is given to the expression of the surface area. Typical order of magnitude of the preceding quantities for collapsed objects of different masses are here estimated.

Mr and Mrs Frank R Kelly of South Pasadena announce the engagement of their daughter, Kathleen, to Dr Demetrios L Christodoulou of Athens, Greece. Kathleen is a graduate of South Pasadena High and Pasadena City College. She will be continuing her studies in nutrition at the University of Athens. Dr Christodoulou is the son of Mr and Mrs Lambros Christodoulou of Athens. He received his degrees from Princeton University, lectured at California Institute of Technology and returned to Athens last fall to accept the 2nd Chair of the Theoretical Physics Department, University of Athens. The wedding will be held the evening of 8 March, in historical settings in Athens. The couple will visit the Isle of Rhodes and then return to Athens to make their home.

The definition of time is established as a fundamental physical principle. From this principle, in connection with the quantum and relativity principles, the laws of quantum geometrodynamics and, in the classical limit, those of general relativity theory, are uniquely deduced.

A decisive turn in my career came in 1977, at a time when I was a postdoctoral fellow at the Max Planck Institute for Astrophysics in Munich. There, Jürgen Ehlers, the leader of the group in which I was working, although himself a physicist, realised that I had a talent in mathematics and gave me an unlimited leave of absence with pay to study mathematics in Paris under the guidance of Yvonne Choquet-Bruhat. Thus, I finally found my true calling and in the period 1977-1981 I studied mathematical analysis in the French school.

This work was sponsored by the "Seminario Matematico dell'Università e Politecnico di Torino." We wish to express our gratefulness to Professor D Galletto and to Professor T Zeuli, who invited one of us (D Christodoulou) to Turin, making our collaboration easier.

The thin sandwich conjecture in the initial value problem of general relativity is investigated by means of differential geometrical methods, in connection to the definition of arc length in a Wheeler superspace. The conjecture is proved to be false by good physical reasons. Its failure on a flat space is related to the "functional dimension" of the superspace and to the behaviour in the linearised theory of quantum gravitation.

I first met Yau in September 1981. I had arrived in New York from Germany a few days earlier for what turned out to be a 2-year visiting membership at the Courant Institute. I knew the Princeton area well because I had been a Ph.D. student in physics in the period 1968-1971, so I looked for housing there, the plan being to commute by train to New York. I sought people at the University and at the Institute and Yau was one of the first people I met. ... my working mathematical knowledge at that point was limited to the field of analysis. I had no working knowledge of geometry. Yau's directness of character and his hands on approach to mathematical problems, cutting through formalities to get to the heart of the matter, won me over from the beginning. He was giving a course on minimal surface theory and applications, in particular the application in the proof of the positive mass theorem, a course which continued for the next academic year. So I decided to stay most of each week at Princeton, follow his course, and learn as much as I could from him.

... for his many basic contributions to rigorous mathematical results in the general theory of relativity. They include: i) the boost theorems which establish the existence of a large class of solutions to Einstein's (and Yang-Mills) equations in a region obtained by boosting the initial Cauchy surface a finite amount; ii) a complete mathematical analysis of the spherical collapse of a scalar field including the structure of the horizons and singularities; and iii) his work with Klainermann on the global existence of solutions to Einstein's equations with weak initial data.

Fortunately, after 2300 years, the Greeks have returned to mathematics!

... for his contributions to the mathematical theory of general relativity.

... for his considerable contribution to the theory of general relativity and gravity.

... for his important contributions to general relativity, especially for his rigorous demonstration of global non-linear stability of Minkowski spacetime.

... for their highly innovative works on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology.

... for pathbreaking contributions to mathematical understanding of the Einstein equations, including fundamental results on black hole formation and the discovery of a nonlinear memory effect in the theory of gravitational radiation, and for introducing a powerful geometric point of view for the problem of shock formation for compressible fluids.

... for his many lasting contributions to the foundation of mathematical physics including the dynamics of relativistic gravitational fields.