About

Vincent Moncrief is a Professor of Physics and of Mathematics at Yale University. His professional affiliation is with the Yale Center for Astronomy and Astrophysics, located at 217 Prospect St, New Haven, CT. The provided information indicates his roles in academia, emphasizing his expertise in physics and mathematics, though specific research focus, background, and key contributions are not detailed in the available text.

Research topics

• Classical mechanics
• Mathematical analysis
• Mathematical physics
• Quantum mechanics
• Physics
• Mathematics
• Theoretical physics
• Statistics

Selected publications

• A Conceptual Introduction To Signature Change Through a Natural Extension of Kaluza-Klein Theory

  ArXiv.org · 2025-10-02

  preprintOpen access1st authorCorresponding

  We propose an extension of basic Kaluza-Klein theory in which the higher-dimensional Lorentzian manifold develops a Cauchy horizon rather than remaining globally hyperbolic as in the conventional framework. In this setting, the $U(1)$-generating Killing field, assumed to exist in Kaluza-Klein theory, undergoes a transition in its causal character, from spacelike in the globally hyperbolic region to timelike in an acausal extension through a horizon. This yields a (lower-dimensional) quotient manifold whose metric changes signature from Lorentzian to Riemannian. In this way, one observes a singular, signature changing transition emerging rather naturally from the projection of a globally smooth, even analytic, Lorentzian geometry ``up in the bundle''. This reveals a ``signature change without signature change'' scenario -- a phrasing inspired by John Wheeler -- and extends the usual Kaluza-Klein framework in a conceptually natural direction.

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• HAMILTONIAN REDUCTION OF EINSTEIN’S EQUATIONS

  Encyclopedia of Mathematical Physics · 2024-10-03

  book-chapterSenior author
  PublisherDOI

• Einstein flow with matter sources: stability and convergence

  Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · 2022 · 2 citations

  1st authorCorresponding
  • Theoretical physics
  • Mathematics
  • Physics

  will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. These studies however did not include matter sources. Therefore, the aim of the present study is to include suitable matter sources and investigate whether one is able to draw a similar conclusion. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.

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• A Positive-Definite Energy Functional for the Axisymmetric Perturbations of Kerr-Newman Black Holes

  arXiv (Cornell University) · 2021 · 3 citations

  1st authorCorresponding
  • Physics
  • Classical mechanics
  • Mathematical analysis

  We consider the axisymmetric, linear perturbations of Kerr-Newman black holes, allowing for arbitrarily large (but subextremal) angular momentum and electric charge. By exploiting the famous Carter-Robinson identities, developed previously for the proofs of (stationary) black hole uniqueness results, we construct a positive-definite energy functional for these perturbations and establish its conservation for a class of (coupled, gravitational and electromagnetic) solutions to the linearized field equations. Our analysis utilizes the familiar (Hamiltonian) reduction of the field equations (for axisymmetric geometries) to a system of wave map fields coupled to a 2+1-dimensional Lorentzian metric on the relevant quotient 3-manifold. The propagating `dynamical degrees of freedom' of this system are entirely captured by the wave map fields, which take their values in a four dimensional, negatively curved (complex hyperbolic) Riemannian target space whereas the base-space Lorentzian metric is entirely determined, in our setup, by elliptic constraints and gauge conditions.

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• A Euclidean signature semi-classical program

  Communications in Analysis and Geometry · 2020-01-01

  preprintOpen accessSenior author

  In this article we discuss our ongoing program to extend the scope of certain, well-developed microlocal methods for the asymptotic solution of Schrdinger's equation (for suitable 'nonlinear oscillatory' quantum mechanical systems) to the treatment of several physically significant, interacting quantum field theories.Our main focus is on applying these 'Euclidean-signature semi-classical' methods to self-interacting (real) scalar fields of renormalizable type in 2, 3 and 4 spacetime dimensions and to Yang-Mills fields in 3 and 4 spacetime dimensions.A central argument in favor of our program is that the asymptotic methods for Schrdinger operators developed in the microlocal literature are far superior, for the quantum mechanical systems to which they naturally apply, to the conventional WKB methods of the physics literature and that these methods can be modified, by techniques drawn from the calculus of variations and the analysis of elliptic boundary value problems, to apply to certain (bosonic) quantum field theories.Unlike conventional (Rayleigh/ Schrdinger) perturbation theory these methods avoid the artificial decomposition of an interacting system into an approximating 'unperturbed' system and its perturbation and instead keep the nonlinearities (and, if present, gauge invariances) of an interacting system intact at every level of the analysis.

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• Could the universe have an exotic topology?

  Pure and Applied Mathematics Quarterly · 2019-01-01 · 3 citations

  preprintOpen access1st authorCorresponding

  A recent article uncovered a surprising dynamical mechanism at work within the (vacuum) Einstein `flow' that strongly suggests that many closed 3-manifolds that do not admit a locally homogeneous and isotropic metric \textit{at all} will nevertheless evolve, under Einsteinian evolution, in such a way as to be \textit{asymptotically} compatible with the observed, approximate, spatial homogeneity and isotropy of the universe \cite{Moncrief:2015}. Since this previous article, however, ignored the potential influence of \textit{dark-energy} and its correspondent accelerated expansion upon the conclusions drawn, we analyze herein the modifications to the foregoing argument necessitated by the inclusion of a \textit{positive} cosmological constant --- the simplest viable model for dark energy.

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• Orbit space curvature as a source of mass in quantum gauge theory

  Annals of Mathematical Sciences and Applications · 2019-01-01

  preprintOpen access1st authorCorresponding

  It has long been realized that the natural orbit space for non-abelian Yang-Mills dynamics is a positively curved (infinite dimensional) Riemannian manifold. Expanding on this result I.M. Singer proposed that strict positivity of the corresponding Ricci tensor (computable through zeta function regularization) could play a fundamental role in establishing that the associated Schroedinger operator admits a spectral gap. His argument was based on representing the (regularized) kinetic term in the Schroedinger operator as a Laplace-Beltrami operator on this positively curved orbit space. We revisit Singer's proposal and show how, when the contribution of the Yang-Mills potential energy is taken into account, the role of the original orbit space Ricci tensor is instead played by a Bakry-Emery Ricci tensor computable from the ground state wave functional of the quantum theory. We next review our ongoing Euclidean-signature-semi-classical program for deriving asymptotic expansions for such wave functionals and discuss how, by keeping the dynamical nonlinearities and non-abelian gauge invariances intact at each level of the analysis, our approach surpasses that of conventional perturbation theory for the generation of approximate wave functionals. Though our main focus is on Yang-Mills theory we derive the orbit space curvature for scalar electrodynamics and prove that, whereas the Maxwell factor remains flat, the interaction naturally induces positive curvature in the (charged) scalar factor of the resulting orbit space. This has led us to the conjecture that such orbit space curvature effects could furnish a source of mass for ordinary Klein-Gordon type fields provided the latter are (minimally) coupled to gauge fields, even in the abelian case. Finally we discuss the potential applicability of our Euclidean-signature program to the Wheeler-DeWitt equation of canonical quantum gravity.

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• Was the Big Bang a Thurston Earthquake in $2+1$ Dimensional Einstein Gravity?

  Notices of the International Consortium of Chinese Mathematicians · 2019-01-01

  article1st authorCorresponding
  PublisherDOI

• Euclidean signature semi-classical methods for bosonic field theories:\n interacting scalar fields

  arXiv (Cornell University) · 2016-01-07

  preprintOpen accessSenior author

  Elegant 'microlocal' methods have long since been extensively developed for\nthe analysis of conventional Schroedinger eigenvalue problems. For technical\nreasons though these methods have not heretofore been applicable to quantum\nfield theories. In this article however we initiate a 'Euclidean signature\nsemi-classical' program to extend the scope of these analytical techniques to\nencompass the study of self-interacting scalar fields in 1 + 1, 2 + 1 and 3 + 1\ndimensions. The basic microlocal approach entails, first of all, the solution\nof a single, nonlinear equation of Hamilton-Jacobi type followed by the\nintegration (for both ground and excited states) of a sequence of linear\n'transport' equations along the 'flow' generated by the 'fundamental solution'\nto the aforementioned Hamilton-Jacobi equation. Using a combination of the\ndirect method of the calculus of variations, elliptic regularity theory and the\nBanach space version of the implicit function theorem we establish, in a\nsuitable function space setting, the existence, uniqueness and global\nregularity of this needed 'fundamental solution' to the relevant, Euclidean\nsignature Hamilton-Jacobi equation for the systems under study. Our methods are\napplicable to (massive) scalar fields with polynomial self-interactions of\nrenormalizable type. They can, as we shall show elsewhere, also be applied to\nYang-Mills fields in 2 + 1 and 3 + 1 dimensions.\n

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• Euclidean signature semi-classical methods for bosonic field theories: interacting scalar fields

  Annals of Mathematical Sciences and Applications · 2016-01-01 · 2 citations

  preprintOpen accessSenior author

  Elegant 'microlocal' methods have long since been extensively developed for the analysis of conventional Schroedinger eigenvalue problems. For technical reasons though these methods have not heretofore been applicable to quantum field theories. In this article however we initiate a 'Euclidean signature semi-classical' program to extend the scope of these analytical techniques to encompass the study of self-interacting scalar fields in 1 + 1, 2 + 1 and 3 + 1 dimensions. The basic microlocal approach entails, first of all, the solution of a single, nonlinear equation of Hamilton-Jacobi type followed by the integration (for both ground and excited states) of a sequence of linear 'transport' equations along the 'flow' generated by the 'fundamental solution' to the aforementioned Hamilton-Jacobi equation. Using a combination of the direct method of the calculus of variations, elliptic regularity theory and the Banach space version of the implicit function theorem we establish, in a suitable function space setting, the existence, uniqueness and global regularity of this needed 'fundamental solution' to the relevant, Euclidean signature Hamilton-Jacobi equation for the systems under study. Our methods are applicable to (massive) scalar fields with polynomial self-interactions of renormalizable type. They can, as we shall show elsewhere, also be applied to Yang-Mills fields in 2 + 1 and 3 + 1 dimensions.

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Recent grants

• Global Studies of Einstein Spacetimes

  NSF · $224k · 2010–2013

• Global Studies of Einstein Spacetimes

  NSF · $195k · 2004–2007

Frequent coauthors

• B. K. Berger

  23 shared

• Arthur E. Fischer

  21 shared

• James Isenberg

  University of Oregon

  19 shared

• Antonella Marini

  14 shared

• Lars Andersson

  12 shared

• Rachel Maitra

  10 shared

• Oliver Rinne

  7 shared

• Jerrold E. Marsden

  6 shared