A Department of Mathematics was first created at King's in 1830, and since then it has established a reputation as a world-leading centre for study and research in pure and applied mathematics.
For example, in the 1960s, Hermann Bondi, Felix Pirani and others working in the field of General Relativity demonstrated beyond doubt the theory that predicted the existence of gravitational waves, overcoming doubts that Einstein himself had had. In the 1970s, David Robinson and Paul Davies made pioneering contributions to the investigation of classical and quantum aspects of the theory of black holes. More recently, the Department has developed network-based filtering techniques which led to new tools to study complex data sets, which are used in both biotech and financial regulation. Researchers in the Department have also developed models and techniques for managing financial risk which are used by both banks and government.
General Relativity in the Department of Mathematics
Between the 1950s and the 1970s general relativity, the theory of gravitation formulated by Albert Einstein in 1915, was transformed into its modern form. Research carried out in the King’s College Mathematics Department during this period made a major contribution to this advance.
At the end of the second world war research in general relativity was at a low ebb. Predicted deviations from Newton’s theory of gravity were so small, and difficult to measure, that there was virtually no experimental work being done in the field and it had little contact with the rest of theoretical physics. However by the time Einstein died in 1955 things were changing. The formation of a small number of significant research groups, in Europe and the United States, was taking place, and there would soon be a renaissance of the subject.
One of these groups was based in the Mathematics Department of King’s College London. At various times throughout the 1920s, 30s and 40s some research on gravitation had been undertaken in the Department by individuals like George Jeffery, George Temple and George McVittie, but Hermann Bondi built a modern research group, the first in the United Kingdom devoted to the study of gravitational physics.
Bondi came to King’s from Cambridge in 1954 as the professor of applied mathematics. He quickly brought his former student Felix Pirani over from Dublin. Together with Clive Kilmister, who was already at King’s, they formed the nucleus of the new group. Generously supported by the U.S. Air Force’s Aerospace Research Laboratories it rapidly became a leading international centre, attracting all the major figures in the field as short or long term visitors. Over the years members of the group investigated many different aspects of general relativity, but probably the two best known ones are gravitational radiation and topics related to black holes.
In 1916 Einstein had predicted the existence of gravitational waves. Subsequently he became uncertain about the physical significance of his results. Surprisingly, doubts about gravitational radiation were still widespread in the 1950s and Bondi was not immune from them.
However in the late 1950s and early 1960s Pirani, Bondi, students and visitors at King’s made major breakthroughs. These demonstrated, unambiguously, how general relativity predicted the existence of gravitational waves and the transfer of energy by gravitational radiation. Several decades later, the first direct observation of gravitational waves was made on 14 September 2015 and was announced by the LIGO and Virgo collaborations on 11 February 2016.
During the second half of the 1960s Bondi was increasingly involved in non-University activities such as defence-related work, and looking at the need for a London flood barrier. His report on the latter led to the Thames Barrier being sited in its current location. In 1967 he was appointed Director-General of the European Space Research Organization. Although he retained his professorship and connection with the College for many years this appointment marked the beginning of his career as a full-time public servant. By that time major discoveries, such as the microwave background radiation and quasars, followed in 1967 by the observation of pulsars, had broadened interest in general relativity and relativistic astrophysics.
Fortunately, new theoretical insights into the global structure of space-time had been emerging. Many were due to Roger Penrose, and later, Stephen Hawking. Penrose was a postdoctoral researcher in the relativity group in the early sixties and even then he was using modern mathematical tools in a highly original way. The new ideas provided a framework within which gravitational radiation, astrophysical dynamics and the gravitational collapse of massive objects to form black holes could be fruitfully investigated.
Research related to black holes was the leading feature of the group’s work on general relativity in the 1970s. David Robinson and Paul Davies came to King’s in the early 70s. Together with their collaborators and students, they made pioneering contributions to the investigation of classical and quantum aspects of the theory of black holes.
The former’s work resulted in major advances in the proofs of the uniqueness of equilibrium black hole solutions of Einstein’s gravitational field equations. The latter made seminal contributions to the theory of quantum fields propagating in curved background space-times, including black hole space-times.
As the 1970s progressed it became clear that, although many interesting and difficult problems remained, there was now a good conceptual and technical understanding of the classical theory of general relativity and research in quantum gravity increased.
Chris Isham came in 1973, and for some years he and his students studied general relativity and quantization in the Department. Research in the Department on fundamental physics incorporating gravity now centres on the study of supersymmetry, string theory, M-theory and related areas.