Black Holes: Excision and Matter Interactions

黑洞：切除和物质相互作用

• 批准号: 0502218
• 负责人: David Neilsen
• 金额: $ 8万
• 依托单位: Brigham Young University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-05-01 至 2008-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0502218&HistoricalAwards=false
• 关键词: Black; Holes; Excision; Matter; Interactions

Numerical solutions of Einstein's equations of general relativity provide the most promising means to understand phenomena associated with strong gravitational fields such as those expected from colliding black holes. This award supports development methods to solve Einstein's equations for black holes using excision to eliminate the black hole interior from the computational domain and a magnetic fluid to model matter interactions in the environment of the black hole. Techniques to be explored and developed include the use of potentially more efficient and stable second-order spatial derivatives in generalized harmonic coordinates, excision with multiple coordinate patches for dynamic spacetimes, and application of numerical methods for conservation equations, such as those for the magnetic fluid, for domains with multiple coordinate patches. Promising discretization schemes and boundary conditions for computational stability will be studied. Initial tests will solve the Einstein equations for axisymmetric black hole spacetimes, eventually leading to head-on collisions of black holes. Astrophysical sources of gravitational radiation must be better understood to fully exploit the gravitational wave data expected from ground-based detectors such as LIGO and the space-based LISA. The numerical techniques developed in this project will have a broader impact on astrophysical fluid dynamics and more generally in computational science, especially in applications where boundaries must be accurately modeled. Furthermore, this project provides significant research opportunities to undergraduate students at Brigham Young University as well as opportunities for them to present scientific results at professional conferences.

爱因斯坦广义相对论方程的数值解提供了最有希望的手段来理解与强引力场相关的现象，例如碰撞黑洞所预期的现象。该奖项支持开发方法，以解决爱因斯坦的黑洞方程，使用切除从计算域中消除黑洞内部，并使用磁流体模拟黑洞环境中的物质相互作用。待探索和开发的技术包括使用可能更有效和更稳定的二阶空间导数在广义调和坐标，切除与多个坐标补丁的动态时空，和应用数值方法的守恒方程，如磁流体，域与多个坐标补丁。有前途的离散计划和边界条件的计算稳定性将进行研究。最初的测试将解决轴对称黑洞时空的爱因斯坦方程，最终导致黑洞的正面碰撞。必须更好地了解引力辐射的天体物理来源，以充分利用LIGO和天基丽莎等地基探测器的引力波数据。在这个项目中开发的数值技术将有更广泛的影响天体物理流体动力学和更普遍的计算科学，特别是在应用程序中的边界必须准确建模。 此外，该项目为杨百翰大学的本科生提供了重要的研究机会，并为他们提供了在专业会议上展示科学成果的机会。