# Yvonne Choquet-Bruhat

Yvonne Choquet-Bruhat (French: [ivɔn ʃɔkɛ bʁy.a] (); born 29 December 1923) is a French mathematician and physicist. Her work lies in the intersection of mathematics and physics, notably in Einstein's general theory of relativity. She is one of the pioneers of the study of general relativity, and particularly known as the first to prove the well-posedness of the Einstein equations. Her work was applied in the detection of gravitational waves.

Yvonne Choquet-Bruhat
Yvonne Choquet-Bruhat in 2006
Born29 December 1923 (age 96)
Lille, France
NationalityFrench
Alma materÉcole Normale Supérieure
CNRS
Known forProving the local existence and uniqueness of solutions to the vacuum Einstein Equations
First woman to be elected to the Académie des Sciences Française
AwardsGrand Officier of the Légion d'honneur
Scientific career
FieldsMathematics, physics
InstitutionsCNRS and others

She was the first woman to be elected to the Académie des Sciences Française ("French Academy of Sciences") and is a Grand Officier of the Légion d'honneur.[1]

## Education

Yvonne was born in Lille in 1923.[2] Her mother was the philosophy professor Berthe Hubert, her father was the physicist Georges Bruhat (1887–1945), who died in the concentration camp Oranienburg-Sachsenhausen, and her brother was the mathematician François Bruhat. Yvonne Choquet-Bruhat undertook her secondary school education in Paris. In 1941 she entered the Concours General, a competition to determine the best pupils in all of France, and won the silver medal for physics. From 1943 to 1946 she studied at the École Normale Supérieure ("ENS") in Paris and from 1946 was a teaching assistant there and undertook research advised by André Lichnerowicz. From 1949 to 1951 she was a research assistant at the French National Centre for Scientific Research ("CNRS"), as a result of which she received her doctorate.[3]

## Career

Yvonne Choquet-Bruhat has worked in a range of areas in mathematical physics, applying results from the analysis of partial differential equations and differential geometry to provide a firm basis for solutions in physics. From 1951-1952 she worked at the Institute for Advanced Study in Princeton, under the supervision of Albert Einstein, where she proved the local existence and uniqueness of solutions to the vacuum Einstein Equations.[4] Her work proves the well-posedness of the Einstein equation, and started the study of dynamics in General Relativity.

Choquet-Bruhat at the University of California, Berkley, in 1974.

The following year Yvonne Choquet-Bruhat joined the faculty at Marseilles and in 1958 she was awarded the CNRS Silver Medal.[5] From 1958 to 1959 she taught at the University of Reims. In 1960 she became a professor at the Université Pierre-et-Marie-Curie (UPMC) in Paris, and has remained professor or professor emeritus until her retirement in 1992.

At the Universite Pierre et Marie Curie she continued to make significant contributions to mathematical physics, notably in general relativity, supergravity, and the non-Abelian gauge theories of the standard model. Her work in 1981 with Demetrios Christodoulou showed the existence of global solutions of the Yang-Mills, Higgs, and Spinor Field Equations in 3+1 Dimensions.[6] Additionally in 1984 she made perhaps the first study by a mathematician of supergravity with results that can be extended to the currently important model in D=11 dimensions.[7]

In 1978 Yvonne Choquet-Bruhat was elected a correspondent to the Academy of Sciences and on 14 May 1979 became the first woman to be elected a full member. From 1980 to 1983 she was President of the Comité international de relativité générale et gravitation ("International committee on general relativity and gravitation"). In 1985 she was elected to the American Academy of Arts and Sciences. In 1986 she was chosen to deliver the prestigious Noether Lecture by the Association for Women in Mathematics.

## Choquet-Bruhat's theorem

Choquet-Bruhat's main theorem is one of the milestones of mathematical general relativity. Her theorem indeed establishes that General relativity has a well-posed initial value formulation.

The theorem says the following: given initial data for the Einstein equation, which is a triple ${\displaystyle (M,g,K)}$  where ${\displaystyle M}$  is a 3-manifold, ${\displaystyle g}$  a Riemannian metric and ${\displaystyle K}$  a symmetric 2-tensor, which satisfies the constraint equations, there exists a maximal globally hyperbolic spacetime which verifies the Einstein equation with the given initial data.

The proof makes use of a clever choice of coordinates, the wave coordinates (which are the Lorentzian equivalent to the harmonic coordinates), in which the Einstein equation becomes a hyperbolic partial differential equation, for which well-posedness results can be applied.

## Private life

Yvonne Choquet-Bruhat has two daughters and a son, Daniel Choquet. She is a widow; her second husband was Gustave Choquet. She was previously married to Léonce Foures, a professor of mathematics at the Marseille faculty, who had studied with Henri Cartan.[5]

## Major Publications

• Theoreme d'Existence pour Certains Systemes d'Equations aux Derivees Partielles non Lineaires, Acta Mathematica, 88: 141 (1952)
• Theoremes d'Existence en Mecanique des Fluides Relativistes, Bulletin de la Soc. Math. de France, 86: 155 (1958)
• Problems and solutions in mathematical physics. Holden Day, San Francisco (1967).
• Géométrie différentielle et systèmes extérieurs. Dunod, Paris 1968.
• Ondes Asymptotiques et Approchees pour des Systemes d'Equations aux Derivees Partielles non Lineaires, J. Maths. Pures et App. 48: 117 (1969)
• Distributions. Théorie et problèmes. Masson, Paris 1973.
• Global Solutions of the Problem of Constraints on a Closed Manifold, Symposia Matematica, (in the series Pubblicazione dell'Istituto Nazionale di Alta Matematica) 12: 317 (1973)
• with Cécile DeWitt-Morette and Margaret Dillard-Bleick: Analysis, manifolds and physics. Elsevier, Amsterdam 1977, revised 1982, ISBN 0-444-50473-7
• with D. Christodoulou, Existence of Global Solutions of the Yang-Mills, Higgs, and Spinor Field Equations in 3+1 Dimensions, Ann. E.N.S. 4th Series 14: 481 (1981)
• Causalite des Theories de Supergravite, Societe Mathematique de France, Asterisque 79-93 (1984)
• Graded bundles and supermanifolds. Bibliopolis, Naples 1989.
• General Relativity and the Einstein Equations, Oxford University Press 2009
• Introduction to General Relativity, Black Holes, and Cosmology, Oxford University Press 2015
• Une Mathématicienne dans cet étrange univers, Odile Jacob 2016, translated as A Lady Mathematician In This Strange Universe: Memoirs, World Scientific 2018

## Awards

• Médaille d'Argent du Centre National de la Recherche Scientifique, 1958
• Prix Henri de Parville of the Académie des Sciences, 1963
• Member, Comite International de Relativite Generale et Gravitation (President 1980-1983)
• Member, Académie des Sciences, Paris (elected 1979)
• Elected to the American Academy of Arts and Sciences 1985
• Association for Women in Mathematics Noether Lecturer, 1986
• Commandeur de la Légion d'honneur, 1997
• Dannie Heineman Prize for Mathematical Physics, 2003
• elevated to the 'Grand Officier' and 'Grand Croix' dignities in the Légion d'Honneur, 2008

## References

1. ^ (in French) Décret of 11 July 2008, published in the JO of 13 July 2008
2. ^
3. ^
4. ^ (in French)Y. Choquet-Bruhat, Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires, Acta math., 88 (1952), pp. 141–225.
5. ^ a b Yvonne Choquet-Bruhat page Archived February 19, 2012, at the Wayback Machine at Contribution of 20th Century Women to Physics pages Archived October 29, 2014, at the Wayback Machine of UCLA
6. ^ "Existence of Global Solutions of the Yang-Mills, Higgs, and Spinor Field Equations in 3+1 Dimensions," (with D. Christodoulou)
7. ^ Causalite des Theories de Supergravite," Societe Mathematique de France, Asterisque 79-93