Vincent Moncrief

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Vincent Moncrief
Vincent Moncrief, 1973 February (portioned).jpg
Moncrief in 1973
CitizenshipAmerican
Alma mater Stanford University (B.S., 1965)
University of Maryland, College Park (Ph.D., 1972)
Known forGauge-invariant black hole perturbation theory
Global existence of Yang–Mills fields (with Eardley)
Hamiltonian reduction of Einstein's equations
Fischer–Moncrief reduced Hamiltonian and the Yamabe invariant
Scientific career
Fields Mathematical physics, general relativity
Institutions Yale University
University of Utah
University of California, Berkeley
Thesis Partially Covariant Quantum Theory of Gravitation  (1972)
Doctoral advisor Charles William Misner
Doctoral students Edward Seidel
Rachel Lash Maitra
Sari Ghanem

Vincent Edward Moncrief is an American mathematical physicist at Yale University, where he is Professor of Physics and of Mathematics. His research centers on general relativity, particularly the global existence and asymptotic behavior of solutions to Einstein's equations, cosmic censorship, and black hole stability.

Contents

Education and career

Moncrief grew up in Oklahoma City. He received his B.S. in physics from Stanford University in 1965 and his Ph.D. in physics from the University of Maryland, College Park in 1972, under the supervision of Charles William Misner. His doctoral dissertation was titled Partially Covariant Quantum Theory of Gravitation. He subsequently held positions at the University of California, Berkeley and the University of Utah before joining Yale.

Research

Black hole perturbation theory

In a series of papers in the mid-1970s, Moncrief developed a gauge-invariant Hamiltonian approach to gravitational perturbation theory for black holes. [1] He decomposed metric perturbations into gauge-invariant and gauge-dependent parts and used the resulting Hamiltonian to establish the stability of both Schwarzschild and Reissner–Nordström black holes. [2] [3] [4] These methods have been widely influential in both analytic and numerical studies of black hole physics.

Global existence of Yang–Mills fields

With Douglas Eardley, Moncrief proved the global existence of solutions to the Yang–Mills equations (coupled to a Higgs field) in (3+1)-dimensional Minkowski space, [5] [6] demonstrating that the curvature remains bounded for all time. This was a landmark result in mathematical physics.

Hamiltonian reduction and the Yamabe invariant

With Arthur Fischer (University of California, Santa Cruz), Moncrief showed that the reduced Hamiltonian for Einstein's equations is related to the Yamabe invariant (sigma constant) of the spatial manifold, and that it is monotonically decreasing along all solutions in the direction of cosmological expansion. [7] This established a connection between the dynamics of general relativity and the topology of the underlying spatial manifold, with implications for the geometrization conjecture. Related work with Lars Andersson and Yvonne Choquet-Bruhat was presented at the Cargèse summer school on 50 years of the Cauchy problem in general relativity.

Moncrief also carried out a Hamiltonian reduction of Einstein's equations in 2+1 dimensions, expressing the dynamics as a system over Teichmüller space. [8]

Cosmic censorship and the Einstein flow

Moncrief's more recent research focuses on the global existence and asymptotic properties of cosmological solutions of Einstein's equations and the question of how these depend on the topology of spacetime. This includes work on Penrose's cosmic censorship conjecture and the study of the "Einstein flow" on various manifolds, including the question of whether the universe could have an exotic spatial topology. [9] He has developed light-cone and higher-order energy estimates, extending methods that proved successful for the classical Yang–Mills equations to the gravitational setting. He also works on Euclidean-signature semi-classical methods for quantum field theory and quantum cosmology. [10]

Selected doctoral students

According to the Mathematics Genealogy Project, Moncrief's doctoral students include Thomas A. Moore (1981), Roger Ove (1986), Edward Seidel (1988), John Cameron (1991), Rachel Lash Maitra (2007), Sari Ghanem (2014), and Joseph Bae (2015). [11]

Recognition

A special issue of Classical and Quantum Gravity titled Spacetime Safari: Essays in Honor of Vincent Moncrief on the Classical Physics of Strong Gravitational Fields was published in recognition of his contributions to mathematical relativity. [12]

References

  1. ↑ Moncrief, Vincent (1974). "Gravitational perturbations of spherically symmetric systems. I. The exterior problem". Annals of Physics . 88 (2): 323–342. Bibcode:1974AnPhy..88..323M. doi:10.1016/0003-4916(74)90173-0.
  2. ↑ Moncrief, Vincent (1974). "Odd-parity stability of a Reissner-Nordström black hole". Physical Review D . 9 (10): 2707–2709. Bibcode:1974PhRvD...9.2707M. doi:10.1103/PhysRevD.9.2707.
  3. ↑ Moncrief, Vincent (1974). "Stability of Reissner-Nordström black holes". Physical Review D . 10 (4): 1057–1059. Bibcode:1974PhRvD..10.1057M. doi:10.1103/PhysRevD.10.1057.
  4. ↑ Moncrief, Vincent (1975). "Gauge-invariant perturbations of Reissner-Nordström black holes". Physical Review D . 12 (6): 1526–1537. Bibcode:1975PhRvD..12.1526M. doi:10.1103/PhysRevD.12.1526.
  5. ↑ Eardley, Douglas M.; Moncrief, Vincent (1982). "The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. I. Local existence and smoothness properties". Communications in Mathematical Physics . 83 (2): 171–191. Bibcode:1982CMaPh..83..171E. doi:10.1007/BF01976040.
  6. ↑ Eardley, Douglas M.; Moncrief, Vincent (1982). "The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. II. Completion of proof". Communications in Mathematical Physics . 83 (2): 193–212. Bibcode:1982CMaPh..83..193E. doi:10.1007/BF01976041.
  7. ↑ "Cargèse Summer School". fanfreluche.math.univ-tours.fr. Retrieved 2016-08-05.
  8. ↑ Moncrief, Vincent (1989). "Reduction of the Einstein equations in 2+1 dimensions to a Hamiltonian system over Teichmüller space". Journal of Mathematical Physics . 30 (12): 2907–2914. Bibcode:1989JMP....30.2907M. doi:10.1063/1.528475.
  9. ↑ Moncrief, Vincent; Mondal, Puskar (2019). "Could the universe have an exotic topology?". Pure and Applied Mathematics Quarterly. 15 (3): 921–966. doi:10.4310/PAMQ.2019.v15.n3.a7.
  10. ↑ Moncrief, Vincent (2015). "Euclidean-signature semi-classical methods for quantum cosmology". Surveys in Differential Geometry XX: One Hundred Years of General Relativity.{{cite book}}: Unknown parameter |editors= ignored (|editor= suggested) (help)
  11. ↑ Vincent Moncrief at the Mathematics Genealogy Project
  12. ↑ Isenberg, James (2004). "Vincent Moncrief and mathematical relativity". Classical and Quantum Gravity . doi:10.1088/0264-9381/21/3/E01.
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