New Multi-Grid Poisson Solver Developed for Numerical Relativity Simulations of Gravitational Collapse
A team of researchers has developed a new multi-grid Poisson solver for numerical relativity, demonstrating its use in simulating the gravitational collapse of a 9-solar-mass star up to core bounce. The solver enables constraint-preserving regridding, improving spatial resolution during simulations while conserving key physical quantities such as baryonic mass and ADM mass to within 0.001–0.1% accuracy. This advance could improve the fidelity of numerical-relativity simulations involving neutron stars, black holes, and core-collapse supernovae.
Researchers led by Kenta Kiuchi have introduced a grid-based multi-grid Poisson solver designed for use within numerical relativity frameworks, addressing a longstanding challenge in maintaining constraint satisfaction while adaptively refining computational grids. The solver was validated against several standard test cases, including two-puncture black hole initial data, static and rotating neutron stars in equilibrium, and a gravitationally collapsing massive star. As a primary demonstration, the team performed a neutrino-radiation-transfer hydrodynamics simulation of the collapse of a 9-solar-mass star, tracking the system through core bounce. By employing a constraint-preserving regrid prescription with the new solver, the simulation preserved baryonic mass to O(10⁻³)% accuracy and ADM mass and angular momentum to O(10⁻²)–O(10⁻¹)% accuracy. These conservation properties are critical for long-duration, high-resolution simulations of compact object formation and gravitational wave source modeling. The work, submitted to arXiv on June 10, 2026, spans 11 pages and 8 figures and is listed under high-energy astrophysical phenomena and general relativity.
What's missing
The paper has not yet undergone peer review, as it is a preprint submitted to arXiv. It is also unclear whether the solver has been tested beyond core bounce, where post-bounce dynamics and long-term stability could introduce additional numerical challenges.
What different sources said
- arXiv astro-phCenter
Implementation of multi-grid Poisson solver in numerical relativity and its application to gravitational collapse of massive star
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