Black Holes: Excision and Matter Interactions

爱因斯坦广义相对论方程的数值解为理解与强引力场相关的现象提供了最有希望的手段，例如黑洞碰撞所产生的引力场。该奖项支持开发方法来解决爱因斯坦的黑洞方程，使用切除从计算领域消除黑洞内部，并支持磁性流体来模拟黑洞环境中的物质相互作用。有待探索和开发的技术包括在广义调和坐标中使用潜在更有效和更稳定的二阶空间导数，动态时空中的多坐标块切除，以及对具有多个坐标块的区域应用守恒方程的数值方法，例如磁性流体的守恒方程。将研究有希望的离散化方案和计算稳定性的边界条件。最初的测试将解出轴对称黑洞时空的爱因斯坦方程，最终导致黑洞的迎头相撞。必须更好地了解引力辐射的天体物理来源，才能充分利用来自LIGO和LISA等地面探测器的引力波数据。在这个项目中开发的数值技术将对天体物理流体动力学以及更广泛的计算科学产生更广泛的影响，特别是在必须准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，并为他们在专业会议上展示科学成果提供了机会。

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.