CAREER: Towards Precision Tests of General Relativity with Black Holes and Gravitational Waves

For over a century, researchers have studied Einstein's theory of general relativity (GR) -- our best understanding of gravity -- with increasing sophistication and precision. With direct detections of gravitational waves (GWs) from Advanced LIGO and Virgo, it is now possible to test GR in the fully nonlinear, dynamical, strong-field regime when black holes (BHs) merge with each other.

Gravitational-wave detection also opens the possibility to observe more subtle aspects of GR, like the permanent deformation to spacetime ("memory") after a GW passes. Both these new tests and the subtle effects of memory require higher precision predictions and more careful calculations than before. Specifically, to carry out precision tests of GR requires performing supercomputer simulations of merging BHs, both in GR and in theories beyond GR.

One aspect of improving the precision of tests of GR is gaining a deeper understanding of subtle effects in GR simulations, such as the fundamental coordinate freedom in GR, that makes it more difficult to compare between independent simulations. Part I of the research component of this award is to better understand these GR subtleties. As for simulations beyond GR, the PI and collaborators have developed a technique for classes of theories that are "close" to GR, but these simulations have not yet been advanced to the level of sophistication of GR simulations.

Part II of the research component of this award will advance the state of the art of beyond-GR simulations. Simultaneously and independently, the educational component of this award will support development of interactive visualization to help educators teach GR and GWs to a broader audience. These interactive tools will be made available online to reach beyond classroom education.

Part I of the research component consists of studies intending to push numerical relativity waveforms to higher precision, not by improving resolution or simulation methods, but rather by capturing a number of subtle effects. These studies include: (i) high-precision multi-mode quasinormal ringdown fits, especially for precessing systems, with the goal of ultimately building a ringdown surrogate model; (ii) developing a framework for comparing waveforms after modeling out by transformations of the Bondi–Van der Burg–Metzner–Sachs (BMS) group, for apples-to-apples comparisons between simulations performed in different gauges, and for better hybridization with post-Newtonian or effective-one-body waveforms; (iii) statistically validating BMS (non-)conservation laws; and (iv) explaining the existence of an approximate symmetry of outgoing radiation from quasi-circular binary inspirals.

Part II of the research component focuses on advancing the state-of-the-art in simulating binary BH mergers beyond-GR theories of gravity. This program includes: (i) bringing generation of beyond-GR waveforms into "production" mode; (ii) controlling the growth of secular effects (due to using perturbation theory) by applying the numerical dynamical renormalization group; (iii) building a surrogate model for beyond-GR waveforms; and (iv) validating this machinery by applying it to scalar-tensor theory, which can also be treated without recourse to perturbation theory.

Finally, the educational component involves producing interactive visualizations to help teach the principles of GR and GW physics. These interactive visualizations will include particles orbiting around BHs, how GWs deform spacetime, how GWs get projected onto LIGO antenna patterns, and even how GWs from a BBH change as the intrinsic and extrinsic parameters are varied.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.