Studies in strong gravitational fields with the aid of computer algebra

经典广义相对论（GR）的未来涉及到在天体物理学感兴趣的情况下，以及在提出关于GR与量子力学整合的基本问题的情况下，面对引力场的全部非线性方面。申请人沿着几名学生开发了GRTensor，这是全球GR和相关领域使用最广泛的计算机代数系统。GRTensor中集成的两个关键特性对其普及至关重要。首先，标准对象库可以通过一种以自然语言定义新对象的工具轻松扩展。第二，计算可以在任意维度的空间中进行，也可以同时在多个时空中进行。GRTensorJ允许GRTensor在本地或通过www交互式运行，具有易于编程的省时界面。这反映了符号计算的客户端的未来：没有学习曲线，没有软件更新和代替文档的内在知识库。我的研究工作的主要目的是确保GRTensorIII在合理的时间范围内准备好公开发布。例如，GRTensor的这个新版本将包括：（i）更紧密地集成和显著增强更高维度的计算，（ii）更紧密地集成数值相对论社区的需求，（iii）对junction包的重大改进和更新，以及（iv）远离依赖商业计算机代数系统的重要一步。我相信GRTensor在研究和教学方面为GR及相关领域做出了重大贡献。它的发展已经并将继续以一种重要的方式促进人力资源规划人员的培训。重新分配练习：2000-2002年-空间、天文学和相对论，相对论部分，指出三个中心领域：（1）天体物理学研究;（2）计算方法;（3）量子引力。 我希望看到GRTensor仍然是我们领域的首选工具，并继续为这三个领域做出重大贡献。我还对天体物理学的两个重要领域感兴趣并做出了贡献：暗物质问题和暗能量难题。

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.