Quasinormal modes and gravitational waves

受扰动的黑洞通过一种被称为“准正常振荡”的过程衰变回它们的基态：产生的引力波既表现出振荡行为，又表现出指数衰减，其特征是离散的复数谱。随着引力波探测器的改进，准正常振铃有望成为引力波天文学的重要观测信号。Vasy和Warnick等人最近的数学工作提供了对这一光谱的更好的数学理解，以及计算准正常频率的新方法。该项目的目标将是采用数学文献中的方法，以更好地理解黑洞的准正则谱如何决定几何形状。人们可能会认为这是光谱理论中经典问题的天体物理学版本：你能听到鼓的形状吗？

Disturbed black holes decay back to their ground state through a process known as 'quasinormal ringdown': gravitational waves are produced which exhibit both oscillatory behaviour and exponential decay, characterised by a discrete spectrum of complex numbers. With improvement in gravitational wave detectors, quasinormal ringdown is expected to be an important observational signal for gravitational wave astronomy. Recent mathematical work of Vasy and Warnick among others has provided an improved mathematical understanding of this spectrum as well as new approaches to compute the quasinormal frequencies. The goal of this project will be to adapt methods from the mathematical literature to better understand how the quasinormal spectrum of a black hole determines the geometry. One may think of this as an astrophysical version of the classical question from spectral theory: 'can you hear the shape of a drum'.