Research

Last updated: September 14, 2026.

The award connects the geometry of hyperboloidal surfaces with the analysis and computation of waves on unbounded domains.

Results

Geometry and time coordinates. Hyperbolic times in Minkowski space (American Journal of Physics, 2024) explains the geometry of hyperboloidal time functions in flat spacetime. Bridging time across null horizons (General Relativity and Gravitation, 2025) connects horizon-penetrating and hyperboloidal coordinates in a common framework for treating null boundaries.

Black-hole oscillations and gravitational waves. With Rodrigo Panosso Macedo, I reviewed the geometric regularization of black-hole oscillations in Hyperboloidal approach to quasinormal modes (Frontiers in Physics, 2025). Our collaborative study Late-time tails in nonlinear evolutions of merging black holes (Physical Review Letters, 2025) identifies tails in fully nonlinear simulations and compares them with perturbative calculations.

Scattering on unbounded domains. A null infinity layer for wave scattering (SIAM Journal on Scientific Computing, 2026) develops a compactified treatment of time-harmonic scattering that computes the far-field pattern directly. The paper demonstrates finite difference, spectral, and finite element implementations.

The award publication list brings together the papers associated with this project. Journal references, preprints, and downloadable citations are available on the individual publication pages.

Research areas

The broader program investigates five connected areas:

• Relativistic Perturbations
• Numerical Analysis
• Scattering Problems for Engineering
• Nonlinear Einstein Equations
• Hyperboloidal Holography

For executable examples and introductions to the methods, see the educational resources.