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感兴趣的情况下面对引力场的完全非线性方面，以及在提出关于广义相对论与量子力学集成的基本问题的情况下。申请者与几名学生一起开发了GRT--全球最广泛使用的计算机代数系统GR及相关领域。两个关键功能被集成到GRT Spetter中，这是它受欢迎的关键。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，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通过一个易于编程的省时界面，允许GRT在本地或在WWW上以交互方式运行。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，并且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，这一新版本的GRC将包括：(I)更紧密地集成和显著增强更高维度的计算，(Ii)更紧密地集成到数值相对论社区的需要，(Iii)对连接包的重大改进和更新，以及(Iv)摆脱对商业计算机代数系统的依赖的重要一步。我相信，无论是在研究领域还是在教学领域，GR都为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的培训做出重大贡献。重新分配练习：2000-2002--空间、天文和相对论，相对论部分，指出了三个核心领域：(1)天体物理研究；(2)计算方法；(3)量子引力。我打算看到GRT仍然是我们领域的首选工具，并继续为所有三个领域做出重大贡献。我还对天体物理学中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.