General Relativity

Robert Geroch​Robert P. Geroch

Ph.D., Princeton, 1967.
Professor, Dept. of Physics, Enrico Fermi Institute, Committee on Conceptual Foundations of Science, and the College.
Theoretical physics, general relativity.

My research interests have been in three areas. The first is in the structure of the partial differential equations of physics. It turns out that there is a class of such equations (called first-order, quasilinear, hyperbolic systems) that, apparently, is sufficiently broad to encompass the descriptions of all (classical) physical systems. This class leads to a "universal" formulation of physical field theories. The second is the issue of describing quantum systems via Feynmann path integrals. There has been found a class of evolution operators for which such path integrals do exist, and this class of evolution operators, remarkably enough, includes candidates that are "close," in a suitable sense, to all bounded operators. Thus, this framework provides justification for the path-integral formulation of quantum mechanics. The third -- an outgrowth of the second -- involves the broad mathematical structure of measure and integration theory. It turns out that there is a framework for this subject -- in which, for example, both the measures and the functions to be integrated are valued in abelian topological groups -- sufficiently broad to encompass all physical applications of measure and integration, yet sufficiently narrow that the subject can be developed within this framework.

Selected Publications:

  • Asymptotic Structure of Space-time. R. Geroch. In Asymptotic Structure of Space-time, eds. T.P. Esposito and L. Witten, Plenum Press, 1977.
  • General Relativity from A to B. R. Geroch. University of Chicago Press, 1978.
  • Distorted Black Holes. R. Geroch and J.B. Hartle. J. Math. Phys. 23, 680, 1982.
  • Dissipative Relativistic Fluid Theories of Divergence Type. R. Geroch, L. Lindblom. Phys. Rev. D 4l, 1855, l990.
  • Total Mass-Momentum of Arbitrary Initial-data sets in General Relativity. R. Geroch, S.M. Perng. J. Math. Phys 35, 4l57, l994.
  • Relativistic Theories of Dissipative Fluids. R. Geroch. J. Math. Phys. 36, 4226, 1995.
  • Partial Differential Equations of Physics. R. Geroch. In General Relativity, Scottish Universities Summer School in Physics, 1996.

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Wald​Robert M. Wald

Chairman of the Department of Physics
Ph.D., Princeton, 1972.
Charles H. Swift Distinguished Service Professor, Dept. of Physics, Enrico Fermi Institute, and the College.
Theoretical physics, general relativity.

My research has been concerned with a broad range of topics in classical general relativity, cosmology, and quantum phenomena related to gravity. A great deal of my research has focused on the theory of black holes---regions of spacetime where gravity is so strong that nothing can escape---and the remarkable (mathematical and physical) analogy between the laws of black hole physics and the ordinary laws of thermodynamics. In particular, the fact that black holes radiate as perfect black bodies as a consequence of quantum particle creation effects has led to many deep insights into the nature of quantum gravity. My interests also span mathematical investigations of classical general relativity, and applications of general relativity to cosmology and astrophysics, such as gravitational lensing phenomena and gravitational radiation reaction effects.

In the past few years, my main research efforts have concerned the formulation of quantum field theory in the presence of gravity, i.e., quantum field theory in curved spacetime. In this approach, gravity is treated classically, but all other fields are treated in accord with the principles of quantum field theory. Some major issues of principle arise in the formulation of this theory on account of the lack of Poincare symmetry and the absence of a preferred vacuum state, but it has recently been shown that the theory can be formulated in a fully satisfactory manner. It is my hope that this will provide important clues to the formulation of a fully quantum theory of gravity itself.

Selected Publications:

  • General Relativity. R.M. Wald. University of Chicago Press, 1984.
  • Quantum Fields in Curved Spacetime and Black Hole Thermodynamics. R.M. Wald. University of Chicago Press, 1994.
  • Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy, V. Iyer and R.M. Wald, Phys. Rev. D 50, 846, 1994.
  • Axiomatic Approach to Electromagnetic and Gravitational Radiation Reaction of Particles in Curved Spacetime. T.C. Quinn and R.M. Wald. Phys. Rev. D 56, 3381, 1997.
  • A New Method for Determining Cumulative Gravitational Lensing Effects in Inhomogeneous Universes. R.M. Wald and D.E. Holz, Phys. Rev. D 58, 063 501, 1998.
  • The Thermodynamics of Black Holes, R.M. Wald, Living Reviews in Relativity 4, 2001-6 (2001). gr-qc/9912119.
  • Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime, S. Hollands and R.M. Wald, Commun. Math. Phys. 223, 289 (2001). gr-qc/0103074.
  • Classical Stabilization of Homogeneous Extra Dimensions, S. Carroll, J. Geddes, M. Hoffman, and R.M. Wald, Phys. Rev. D
  • On the Renormalization Group in Curved Spacetime, S. Hollands and R.M. Wald, Commun. Math. Phys. 237, 123 (2003). gr-qc/0209029.
  • Conservation of the Stress Tensor in Interacting Quantum Field Theory in Curved Spacetimes, S. Hollands and R.M. Wald, Rev. Math. Phys. 17, 227 (2005). gr-qc/0404074.

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