Towards precision gravitational wave models with numerical and analytical relativity

The National Science Foundation Division of Physics awarded The University of Mississippi $240,000 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop precision gravitational wave models combining numerical and analytical relativity approaches.

The award funds two research components. Part I involves analytical modeling of inspirals and gravitational wave signals from binary black hole systems on eccentric orbits with misaligned spins, accounting for complex spin and orbital plane precession. These analytical waveforms will be hybridized with numerical relativity supercomputer simulations—a process not previously performed for eccentric spin-precessing systems. Part II focuses on validating numerical relativity codes by benchmarking multiple codes against each other through comparative analysis, including mapping parameter spaces across different simulation methodologies. The award also compares and quantifies waveforms from numerical relativity and black hole perturbation theory, with particular attention to precession effects in extreme mass-ratio binaries where perturbation theory is more practical than full numerical simulation.

Work is performed at The University of Mississippi, University, Mississippi, with a period of performance through July 31, 2029. This project grant is classified as assistance funding to support the theoretical modeling required to extract maximum scientific value from gravitational wave observations as detector sensitivity improves.

Abstract

Gravitational wave (GW) astronomy is now a fully-fledged observational field, allowing US to learn about the fundamental nature of nonlinear, dynamical, strong gravitational fields when pairs of black holes (BHS) merge with each other. These observations may hint at how einstein's theory of general relativity (GR) ultimately breaks, as IT must at higher energies. Extracting as much science as possible from GW observations requires that the theoretical models of GW signals are at least as good as the experimental data, which is slated to improve by orders of magnitude in the next dozen years. This motivates the need to more carefully model yet more extreme systems. Part i of the research for this award is to analytically model the inspirals and GWS from binaries of spinning BHS on eccentric orbits with misaligned spins. This results in extremely complicated precession of the spins and orbital plane, which to date has only been treated approximately. These analytical waveforms can then be combined with the output of numerical relativity (NR) supercomputer simulations, a process called hybridization, which has never been carried out for eccentric spin-precessing systems. Part II of the research for this award focuses on comparisons across multiple NR codes and multiple methodologies. NR codes are so complicated that IT behooves the field to validate their correctness and precision by benchmarking them against each other. An apples-to-apples comparison is only possible after mapping their parameter spaces onto each other, which is nontrivial. This award will construct this mapping and thus compare NR catalogs from different codes to each other. Finally, NR is impractical for binaries with extremely large mass ratios, where the techniques of BH perturbation theory (bhpt) shine. This award will also compare and quantify waveforms from NR and bhpt, focusing in particular on precession for binaries with misaligned spin, which is known to be incomplete in bhpt. Part i of this research component is a major post-newtonian (PN) modeling and hybridization effort. IT involves developing eccentric waveform models ((1) without and (2) with precession of the plane and spins); and (3) incorporating the effects of radiation reaction. All of this is to be done without recourse to averaging, by using near-identity transformations. This sets the stage for these PN results to be incorporated into a robust PN-NR hybridization scheme. Part II of this research component is multiple cross-code and cross-methodology comparisons. The program includes (1) developing common tooling for multiple NR catalogs; (2) mapping different NR catalogs' parameter spaces to a common surrogate reference; (3) generating continuous maps between these catalogs' parameter spaces, and thus comparing them in an apples-to-apples fashion. Then, connecting more with theory, (4) comparing the precession dynamics of precessing inspirals in NR against those computed with the fastemriwaveforms code; and (5) computing the torque and force on the primary in the small mass-ratio limit, which has been ignored so far. Finally, the educational component involves producing interactive visualizations to help teach the principles of GR and GW physics. 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.- subawards are not planned for this award.