Studies in strong gravitational fields with the aid of computer algebra

经典广义相对论（GR）的未来涉及面对引力场的全部非线性方面的情况下，天体物理学的兴趣和情况下提出的基本问题，关于广义相对论与量子力学的整合。申请人与几名学生一起开发了GRTensor，这是世界上最广泛使用的GR及相关领域的计算机代数系统。集成到GRTensor中的两个关键特性是其受欢迎的关键。首先，标准对象库很容易通过用自然语言定义新对象的工具进行扩展。其次，可以在任意维度的空间和多个时空中同时进行计算。GRTensorJ允许GRTensor在本地或www上以交互方式运行，具有易于编程的节省时间的界面。这反映了符号计算客户端的未来：没有学习曲线，没有软件更新，有一个内在的知识库来代替文档。我的研究工作的主要目的是确保GRTensorIII在合理的时间框架内准备好公开发布。例如，GRTensor的新版本将包含：(i)对高维计算的更紧密集成和显著增强，（ii）对数值相对论社区需求的更紧密集成，（iii）对结包的重大改进和更新，以及（iv）远离对商业计算机代数系统的依赖的重要一步。我认为GRTensor在研究和教学方面都对GR及相关领域做出了重大贡献。它的发展已经并将继续对HQP的培训作出重大贡献。《空间、天文学和相对论》，相对论部分，指出了三个中心领域：(1)天体物理研究；(2)计算方法；(3)量子引力。我希望看到GRTensor仍然是我们这个领域的首选工具，并继续为这三个领域做出重大贡献。我对天体物理学的两个重要领域也很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.