Black Holes: Excision and Matter Interactions

爱因斯坦广义相对论方程的数值解提供了最有希望的方法来理解与强引力场相关的现象，比如黑洞碰撞。该奖项支持解决爱因斯坦黑洞方程的开发方法，使用切除将黑洞内部从计算域中消除，并使用磁流体来模拟黑洞环境中的物质相互作用。有待探索和发展的技术包括在广义调和坐标中使用可能更有效和稳定的二阶空间导数，在动态时空中使用多个坐标块进行切除，以及在具有多个坐标块的域中应用数值方法求解守恒方程，例如磁流体的守恒方程。将研究有前途的离散化方案和计算稳定性的边界条件。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，才能充分利用地面探测器（如LIGO和天基LISA）所期望的引力波数据。本项目开发的数值技术将对天体物理流体动力学和更广泛的计算科学产生更广泛的影响，特别是在必须精确模拟边界的应用中。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。

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.