Physics / research
Evolving relativistic spacetimes numerically
Study spacetime decomposition, constraints, gauge choices, evolution formulations, and numerical convergence in simulations of strong gravitational fields.
Your route through physics
Follow the path or begin with a question. Every lesson is open.
Your place, at your pace. Progress is optional and saved only in this browser when available.
Read / explore / reason
Inside this module
Module 01 research
Evolving relativistic spacetimes numerically
Study spacetime decomposition, constraints, gauge choices, evolution formulations, and numerical convergence in simulations of strong gravitational fields.
- 01
Three-plus-one spacetime decomposition
Separate spacetime geometry into spatial data and coordinate evolution with declared normal and curvature signs.
32 min - 02
ADM Hamiltonian and momentum constraints
Test admissible spatial data and distinguish local constraint residuals from numerical convergence.
32 min - 03
Conformal method for initial data
Identify freely specified conformal data and audit elliptic residuals on explicitly limited toy grids.
32 min - 04
Lapse, shift, and coordinate gauge conditions
Calculate local slicing changes and distinguish gauge-characteristic speeds from physical light propagation.
32 min - 05
BSSN and generalized harmonic formulations
Compare evolved variables and the role of hyperbolicity without equating reformulation with a new gravitational theory.
32 min - 06
Constraint damping and boundary treatment
Analyze the limits of damping and the boundary information needed to preserve a constrained evolution.
32 min - 07
Black-hole punctures and excision
Compare two singularity-handling strategies and interpret horizon mass, spin, and characteristic diagnostics.
32 min - 08
Adaptive mesh refinement in spacetime evolution
Count refinement costs and connect time synchronization, interpolation and characteristic resolution.
32 min - 09
Wave extraction and asymptotic observables
Track tetrad conventions, curvature-to-strain integration and finite-radius extrapolation errors.
32 min - 10
Numerical relativity convergence and error budgets
Turn grid comparisons and balance diagnostics into conditional uncertainty estimates for defined observables.
32 min