Studies in strong gravitational fields with the aid of computer algebra

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The future of classical general relativity (GR) involves facing the full nonlinear aspects of the gravitational field in situations of astrophysical interest and in situations that raise fundamental issues regarding the integration of GR with quantum mechanics. The applicant, along with several students, developed GRTensor, the single most widely used computer algebra system for GR and related fields worldwide. Two key features integrated into GRTensor have been critical to its popularity. First, standard object libraries are easily expandable by a facility for defining new objects in a natural language. Second, calculations can be carried out in spaces of arbitrary dimension and in multiple spacetimes simultaneously. GRTensorJ allows GRTensor to be run interactively either locally or over the www with an easily programmable time-saving interface. This reflects the future of the client's side of symbolic computation: no learning curve, no software updates and an intrinsic knowledge base in lieu of documentation. The major thrust of my research effort is to ensure that GRTensorIII is ready for public release in a reasonable time frame. This new release of GRTensor will, for example, incorporate: (i) tighter integration of and significant enhancements to calculations in higher dimensions, (ii) tighter integration to the needs of the numerical relativity community, (iii) major improvements and updates to the junction package, and (iv) a significant step away from reliance on commercial computer algebra systems. I believe that GRTensor has made a significant contribution to GR and related fields in both research and teaching. Its development has and will continue to contribute in a major way to the training of HQP. The Reallocations Exercise: 2000-2002 - Space, Astronomy and Relativity, Relativity section, points out three central areas: (1) astrophysical research; (2) computational methods; (3) quantum gravity.  I intend to see that GRTensor remains the tool of choice in our field and that it continues make significant contributions to all three areas. I am also interested in and have contributed to two important areas in astrophysics: the dark matter problem and the dark energy conundrum.