General Relativity

Robert Geroch ​Robert P. Geroch

Ph.D., Princeton, 1967.
Professor Emeritus, 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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daniel Daniel E. Holz

Ph.D., Chicago, 1998.
Associate Professor, Dept. of Physics, Enrico Fermi Institute, and the College.
general relativity, astrophysics, cosmology.

My research focuses on the interplay of general relativity, astrophysics, and cosmology. Recently my work has concentrated on gravitational waves and gravitational lensing: two uniquely powerful cosmological probes furnished by general relativity.

With the advent of the Laser Interferometer Gravitational-wave Observatory (LIGO), we are on the verge of the era of gravitational-wave astronomy. I have been exploring the capability of LIGO to make cosmologically interesting measurements. In particular, by observing the gravitational-wave driven inspiral of binary compact objects, LIGO can measure the absolute distance to a source. When coupled with independent measurements of redshift, these systems, which we have dubbed "standard sirens", are extremely powerful cosmological probes. I have been especially interested in short/hard gamma-ray bursts as likely standard-siren sources for LIGO.

I have also worked to characterize the effects of gravitational lensing on cosmologically distant sources. All sources beyond a few hundred megaparsecs are gravitationally-lensed, with their observed brightnesses and shapes being altered on average by a few percent or more. These effects are highly non-Gaussian, and I have worked extensively to characterize them. This lensing is particularly relevant for attempts to measure cosmological evolution through standard candles and standard sirens. I have also explored the science that results from measuring this lensing signal.

I have explored a broad range of additional topics, including cosmological N-body simulations, the gravitational-wave rocket effect, population synthesis of black hole binaries and gamma-ray bursts, retro-MACHOs, dark energy phenomenology, and the most massive clusters in the Universe.

Selected Publications:

  • Seeing double: strong gravitational lensing of high-redshift supernovae, D.E. Holz, Astrophys. J. Lett. 556, L71 (2001).
  • Collisional dark matter and scalar phantoms, D.E. Holz & A. Zee, Phys. Lett. B 517, 239 (2001).
  • Retro-MACHOs: π in the sky?, D.E. Holz & J.A. Wheeler, Astrophys. J. 578, 330 (2002).
  • Gravitational wave emission from core-collapse of massive stars, C.L. Fryer, D.E. Holz, & S.A. Hughes, Astrophys. J. 565, 430 (2002).
  • Using gravitational-wave standard sirens, D.E. Holz & S.A. Hughes, Astrophys. J. 629, 15 (2005).
  • Short GRB and binary black hole standard sirens as a probe of dark energy, N. Dalal, D.E. Holz, S.A. Hughes, B. Jain, Phys. Rev. D 74, 063006 (2006).
  • Ultra-high precision cosmology from gravitational waves, C. Cutler & D.E. Holz, Phys. Rev. D 80, 104009 (2009).
  • On The Origin Of The Highest Redshift Gamma-Ray Bursts, K. Belczynski, D.E. Holz, C.L. Fryer, E. Berger, D.H. Hartmann, & B. O’Shea, Astrophys. J. 708, 117 (2010).
  • The most massive objects in the Universe, D.E. Holz & S. Perlmutter, arXiv/1004.5349.

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Wald ​Robert M. Wald

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.

In the past few years, one of my main research efforts has 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.

Another main research effort has concerned self-force (or “radiation reaction”) effects on the motion of small bodies in classical general relativity. These effects must be fully understood to predict the gravitational radiation emitted by, say, a small black hole as it inspirals into a large black hole. The notion of a “point particle” does not make sense in general relativity, but one can consider a limit wherein a body's mass as well as its size shrinks to zero in an asymptotically self-similar manner. Self-force effects can then be rigorously derived as a perturbative correction to geodesic motion, and self-consistent schemes for determining motion and radiation can then be developed.

Another recent main research effort has concerned has concerned analysis of the effects of small scale inhomogeneities in classical general relativity, as is needed for applications to cosmology. A new perturbative framework was developed that allows nonlinear effects to be important on small scales. This framework was used to show that small scale inhomogeneities cannot produce accelerated expansion of the universe, as had been suggested by a number of authors.

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.
  • The Thermodynamics of Black Holes, R.M. Wald, Living Reviews in Relativity 4, 2001-6 (2001). gr-qc/9912119.
  • Axiomatic Quantum Field Theory in Curved Spacetime, S. Hollands and R.M. Wald, Commun. Math. Phys. 293, 85 (2010). arXiv:0803.2003.
  • A Rigorous Derivation of Gravitational Self-force, S.E. Gralla and R.M. Wald. Class.Quant.Grav. 25, 205009, 2008. arXiv:0806.3293.
  • A new framework for analyzing the effects of small scale inhomogeneities in cosmology. S.R. Green and R.M. Wald, arXiv:1011.4920.

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Updated 2/2011

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