White Paper: Mathematical and Computational Challenges in the Era of Gravitational-wave Astronomy
This white paper is an outcome of IPAM’s fall 2021 long program, Mathematical and Computational Challenges in the Era of Gravitational Wave Astronomy.
On September 14, 2015, a worldwide effort of countless of scientists that had started one hundred years earlier with Einstein’s formulation of the Theory of General Relativity (GR) came to a climax with the LIGO and Virgo’s historic detection of GWs from a pair of colliding black holes (BHs). GWs are dynamical changes in the curvature of spacetime. Their astrophysical and cosmological sources are cataclysmic events, such as coalescing binary systems of BHs and supernovae explosions. Less than two years after the first detection, LIGO and Virgo observed GWs from a pair of neutron stars (NSs), ushering a new era of multi-messenger astrophysics (MMA). The most recent LIGO-Virgo-KAGRA (LVK) GW transient catalog includes a total of 90 detections of compact binary coalescences (CBCs). These observations provide physicists with a plethora of new physical information, from testing GR in the strong field regime to using new ways of measuring the expansion of the universe to exploring the properties and dynamics of matter in extreme densities.
Because of the extreme sensitivity of the detectors and the complexity of the physics involved, the extraction of physical information from the data is very challenging. The process that leads from signal detection to their physical interpretation requires a synergy of expertise encompassing instrumental science, mathematics, fundamental physics, astrophysics, and computer science.
Construction of accurate theoretical models is one of the main requirements to identify and interpret the observed GW signals. This involves a deep mathematical knowledge and a synergy between analytic and numerical techniques to solve the field equations of GR. In the presence of matter, such as in NSs, GR must be combined with additional physics, such as magnetohydrodynamics (MHD).
Confident detection of GW signals and the extraction of their physical information are computationally intensive. Therefore, the development of fast and robust tools to increase the speed of these processes is crucial for the GW community and bound to become even more critical as the sensitivity of current detectors improves and next-generation detectors come online.
Machine learning (ML) is a common tool for all these topics.
The aim of this IPAM long program was to connect these many facets of GW science and MMA by bringing together some of the foremost mathematicians, physicists and computer scientists working in the GW community. The program was designed with a structure mimicking the complex process that leads from first mathematical principles in GR to the physical interpretation of GW observations. Thus the program consisted of four workshops (WSs), each addressing one of the main aspects of the GW science:
- WS I “Computational Challenges in Multi-Messenger Astrophysics” focused on the physics of source dynamics of future detections of GW signals and the generation of accurate GW templates.
- WS II “Mathematical and Numerical Aspects of Gravitation” focused on the mathematics of the equations governing relativistic systems.
- WS III “Source Inference and Parameter Estimation in Gravitational-Wave Astronomy” focused on current, state-of-the-art approaches for parameter estimation in MMA.
- WS IV “Big Data in Multi-Messenger Astrophysics” focused on the development of ML techniques for a more efficient handling of GW data sets, reduction of detector noise, identification of astrophysical signals, and increase in detection confidence.
Given the interconnection between the topics covered in the four WSs, this document has been organized into the following sections: Mathematics of spacetime, numerical relativity (NR), GW data analysis, and physical interpretation of GW observations.