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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 which describes closed, inhomogeneous universes which
contain gravitational wave modes of arbitrary wavelengths. These solutions,
which have come to be called 'Gowdy universes', are essentially gravitational
-waves 'in a box' --- i.e. with periodic boundary conditions. They have
proven to be useful examples of gravitational wave dynamics.
Selected Publications
- 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.
Geometrical Physics
My current research is 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
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