Robert H. Gowdy

Associate Professor Mathematical Physics and Astrophysics (804) 828-1821 rgowdy@vcu.edu

Education

Research Interests

Einstein's Theory of General Relativity is at once a theory of gravity and a theory of space and time. One of its predictions is that extreme astrophysical events such as supernova explosions and the mutual capture of neutron stars and black holes will emit gravitational waves --- ripples in the geometry of space and time. Large instruments to detect such waves are under construction at many sites around the world. Efforts to predict exactly what those instruments will observe depend on numerical simulations of the space and time near very complex astrophysical sources. A typical example of such a possible source of gravitational waves would be a pair of black holes spiralling in towards each other and merging to form one, larger, black hole.

The numerical simulation of what Einstein's Field Equations predict about the behavior of space and time in extreme situations has proven to be a very difficult problem. An important validation test for these numerical simulation routines is to see if they can reproduce known exact solutions of Einstein's Field Equations. Gowdy spacetimes, discovered in 1974, have become standard tests for these routines because they are among the most complex exact solutions known.

After fifty years of continuous effort by many people, numerical routines can now give accurate simulations of the spacetime near an astrophysical source of gravitational waves. The difficulty that remains is called "wave extraction" and refers to the process of connecting near-field events to the gravitational waves that would be detected far from those events. Several competing wave extraction techniques are being tried. The 1974 Gowdy spacetimes cannot be used to test the accuracy of these techniques because they are closed universes with no "outside" for radiation to spread into. A new family of exact solutions, found in 2007, has waves spreading to infinity and decreasing in amplitude in the same was as waves from a realistic astrophysical source. Those solutions are now under study and may provide useful ways to validate wave extraction techniques.

Selected Publications

Gowdy, R. H, B. Douglas Edmonds: "Cylindrical Waves in Expanding Universes: Models for Compact Sources," Physical Review 75. 084011, 2007

Robert H. Gowdy, "Of gravitational waves and spherical chickens," article in Einstein Online (Max Planck Institute for Gravitational Physics, Potsdam Germany.
http://www.einstein-online.info/en/spotlights/gowdy_st/

Robert H. Gowdy, "General Relativity" article in The MacMillan Encyclopedia of Physics,(John S. Rigden ed., MacMillan, 1996), pp. 5146-5151

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.