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Yvonne Choquet-Bruhat | |
|---|---|
_(cropped).jpg) Choquet-Bruhat in 1974 | |
| Born | Yvonne Suzanne Marie-Louise Bruhat (1923-12-29)29 December 1923 |
| Died | 11 February 2025(2025-02-11) (aged 101) Mérignac, France |
| Alma mater | |
| Known for |
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| Spouses | |
| Children | 3, includingDaniel |
| Awards |
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| Scientific career | |
| Fields | |
| Institutions | Pierre and Marie Curie University |
| Thesis | Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires (1951) |
| Doctoral advisor | André Lichnerowicz |
Yvonne Choquet-Bruhat (French:[ivɔnʃɔkɛbʁy.a]ⓘ; 29 December 1923 – 11 February 2025) was a French mathematician and physicist. She made seminal contributions to the study ofgeneral relativity, by showing that theEinstein field equations can be put into the form of aninitial value problem which iswell-posed. In 2015, her breakthrough paper was listed by the journalClassical and Quantum Gravity as one of thirteen 'milestone' results in the study of general relativity, across the hundred years in which it had been studied.[1]
Choquet-Bruhat was the first woman to be elected to theFrench Academy of Sciences and was a Grand Officer of theLegion of Honour.[2]
Yvonne Bruhat was born inLille on 29 December 1923.[3] Her mother was the philosophy professor Berthe Hubert and her father was the physicistGeorges Bruhat, who died in 1945 in the concentration campOranienburg-Sachsenhausen.[4] Her brotherFrançois Bruhat also became a mathematician, making notable contributions to the study ofalgebraic groups.
Bruhat undertook her secondary school education in Paris earning herBaccalauréat in 1941. She received the prestigiousConcours Général national competition, winning the silver medal for physics. From 1943 to 1946 she studied at theÉcole normale supérieure de jeunes filles in Paris, and from 1946 was a teaching assistant there and undertook research advised byAndré Lichnerowicz.
From 1949 to 1951 Bruhat was a research assistant at theFrench National Centre for Scientific Research, as a result of which she received her doctorate.[5]
In 1951, she became apostdoctoral researcher at theInstitute for Advanced Study inPrinceton, New Jersey. Her supervisor,Jean Leray, suggested that she study the dynamics of theEinstein field equations. He also introduced her toAlbert Einstein, whom she consulted with a few times further during her time at the institute.
In 1952, Bruhat and her husband were both offered jobs atMarseille, precipitating her early departure from the institute. In the same year, she published the local existence and uniqueness of solutions to the vacuumEinstein equations, her most renowned achievement. Her work proves thewell-posedness of the Einstein equations,[4] and started the study of dynamics in general relativity.
In 1958, she was awarded theCNRS Silver Medal.[6] From 1958 to 1959 she taught at theUniversity of Reims. In 1960 she became a professor at theUniversité Pierre-et-Marie-Curie (UPMC) inParis, and remained professor or professor emeritus until her retirement in 1992.
At theUniversite 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 withDemetrios Christodoulou showed the existence of global solutions of the Yang–Mills, Higgs, and spinor field equations in 3+1 Dimensions.[7] Additionally in 1984 she made perhaps the first study by a mathematician ofsupergravity with results that can be extended to the currently important model inD=11 dimensions.[8]
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.[4] From 1980 to 1983 she was President of theComité international de relativité générale et gravitation ("International committee on general relativity and gravitation"). In 1985 she was elected to theAmerican Academy of Arts and Sciences. In 1986 she was chosen to deliver the prestigiousNoether Lecture by theAssociation for Women in Mathematics.
Choquet-Bruhat's best-known research deals with the mathematical nature of the initial data formulation ofgeneral relativity. A summary of results can be phrased purely in terms of standarddifferential geometric objects.
In this sense, an initial data set can be viewed as the prescription of the submanifold geometry of an embedded spacelike hypersurface in a Lorentzian manifold.
One of Choquet-Bruhat's seminal 1952 results states the following:
Every vacuum initial data set(M,g,k) has a developmentf :M → (M,g) such thatg has zeroRicci curvature, and such that every inextendible timelike curve in the Lorentzian manifold(M,g) intersectsf(M) exactly once.
Briefly, this can be summarized as saying that there exists avacuum spacetime(M,g) for whichf(M) is aCauchy surface. Such a development is called aglobally hyperbolic vacuum development. Choquet-Bruhat also proved a uniqueness theorem:
Given any two globally hyperbolic vacuum developmentsf1 :M → (M1,g1) andf2 :M → (M2,g2) of the same vacuum initial data set, there is an open subsetU1 ofM1 containingf1(M) and an open subsetU2 ofM2 containingf2(M), together with an isometryi : (U1,g1) → (U2,g2) such thati(f1(p)) =f2(p) for allp inM.
In a slightly imprecise form, this says: given any embedded spacelike hypersurfaceM of a Ricci-flat Lorentzian manifoldM, the geometry ofM nearM is fully determined by the submanifold geometry ofM.
In an article written withRobert Geroch in 1969, Choquet-Bruhat fully clarified the nature of uniqueness. With a two-page argument inpoint-set topology usingZorn's lemma, they showed that Choquet-Bruhat's above existence and uniqueness theorems automatically imply a global uniqueness theorem:
Any vacuum initial data set(M,g,k) has amaximal globally hyperbolic vacuum development, meaning a globally hyperbolic vacuum developmentf :M → (M,g) such that, for any other globally hyperbolic vacuum developmentf1 :M → (M1,g1), there is an open subsetU ofM containingf(M) and an isometryi :M1 →U such thati(f1(p)) =f(p) for allp inM.
Any two maximal globally hyperbolic vacuum developments of the same vacuum initial data are isometric to one another.
It is now common to study such developments. For instance, the well-known theorem ofDemetrios Christodoulou andSergiu Klainerman on stability of Minkowski space asserts that if(ℝ3,g,k) is a vacuum initial data set withg andk sufficiently close to zero (in a certain precise form), then its maximal globally hyperbolic vacuum development is geodesically complete and geometrically close toMinkowski space.
Choquet-Bruhat's proof makes use of a clever choice of coordinates, thewave coordinates (which are the Lorentzian equivalent to theharmonic coordinates), in which the Einstein equations become a system ofhyperbolic partial differential equations, for which well-posedness results can be applied.
In 1947, she married fellow mathematician Léonce Fourès. Their daughter Michelle is anecologist. Her doctoral work and early research is under the name Yvonne Fourès-Bruhat. In 1960, Bruhat and Fourès divorced, she later married the mathematicianGustave Choquet and changed her last name to Choquet-Bruhat. She and Choquet had two children; her son,Daniel Choquet, is a neuroscientist and her daughter, Geneviève, is a medical doctor.
Choquet-Bruhat died on 11 February 2025 in Merignac, France (33700), at the age of 101.[9][4]
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