My research has been in the area of General Relativity, Einstein's Theory of Gravitation. I have emphasized the use of geometrical methods to explore the possible solutions of Einstein's Equations. I am probably best known for a family of solutions that describes closed, inhomogeneous universes that contain gravitational wave modes of arbitrary wavelengths. These solutions, which have come to be called 'Gowdy universes', are essentially gravitational -waves 'in a box' ---

Recently, I realized that the methods of my earlier work could be used to construct a new family of solutions to Einstein's Equations. These solutions represent cylindrical gravitational waves in an expanding universe. They are important because the wave amplitudes fall off with distance in the same way as waves from a compact source and the geometry at large distances is that of flat Minkowski spacetime. Thus, they can be used as exact solution models of gravitational waves from compact astrophysical sources.

- Gowdy, R. H.: "Closed Gravitational Wave Universes: Analytic Solutions with
Two-parameter Symmetry,"
*Journal of Mathematical Physics***16**, pp 224-226, 1975. - Gowdy, R. H.: "Vacuum Spacetimes with Two-parameter Spacelike Isometry
Groups and Compact Invariant Hypersurfaces: Topologies and Boundary
Conditions,"
*Annals of Physics*(N.Y.)**83**, pp 203-241, 1974. - Gowdy, R.H. and Edmonds, B.D.: "Cylindrical gravitational waves in expanding universes: Models
for waves from compact sources,"
*Phys. Rev. D15*, in press, 2007

Available from gr/qc e-print Archive

*Geometrical Physics*

I have been developing the idea that the fundamental geometrical structures of many physical problems can be expressed entirely in terms of projection tensor fields, along with a way to take derivatives --- an affine connection. By developing the affine geometry of projection tensor fields, I am finding a single set of insights and identities which apply to a wide variety of different situations. For example, the geometrical theory of surface embedding due to Gauss and Weingarten, fluid dynamics, spacetime perturbation theory, and the dynamics of cosmic strings and membranes are all included in this framework.

*Selected Publications*

- Gowdy, R. H.: "Affine Projection Tensor Geometry: Lie
Derivatives and Isometries,"
*Journal of Mathematical Physics***35**, 1274-1301, 1995.

Available from gr/qc e-print Archive - Gowdy, R. H.: "Affine Projection Tensor Geometry: Decomposing the Curvature
Tensor When the Connection is Arbitrary and the Projection is Tilted,"
*Journal of Mathematical Physics***35**, 1274-1301, 1994.

Available from gr/qc e-print Archive

*Physics Education*

I adapted both our conceptual physics course, Foundations of Physics, and our Astronomy course, so that they can be used to fulfill the new (as of 1997) general education requirement for physical science at VCU. The format of these courses --- large lecture sessions --- was not being changed because that format is the only one which will let us meet the demand with our available resources. I used technology --- specifically the World Wide Web and, more recently, a classroom response system --- to overcome the well-known shortcomings of the large-lecture format. The courses are taught from the home pages Physics and Astronomy on the Web. Those home pages organize the course material into a densely hyperlinked documents which are each used as

- a focus for discussion in class by projecting the material onto a screen.
- an individual tutor with interactive test questions linked to each main point.
- a testing device in class.
- the only required textbook for the class.

*Recent grants and proposals:*

*Virginia Urban Corridor Teacher Preparation Collaborative*, NSF grant for five years, PI: Reuben Farley, Bill Haver, Joe Chinnici, Richard Rezba, $5,000,000, Participant in the Physics component of the grant, 1996-2001.

*Selected Publications*

- Gowdy, R. H.: "The Physics of Perfect Rockets,"
*American Journal of Physics*,**63**, pp229-231, 1995. - Gowdy, R. H., "General Theory of Relativity," article to appear in the
*MacMillan Encyclopedia of Physics*, 1996

Department Faculty Other Research at VCU

Last Reviewed: March 15, 2007

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