Numerical Relativity - Mathematical Formulation by Harald Pfeiffer

Dive into a comprehensive lecture on numerical relativity and the mathematical formulation of simulating coalescing binary black holes. Explore the fundamental concepts of gravitational waves, the history of numerical relativity, and its key components. Learn about the goals of numerical relativity, differential geometry, extrinsic curvature, and adopted coordinates. Examine the decomposition of curvature, partial differential equations, constraint solving techniques, and the BSSN equations. Gain insights into black hole momentum and spin, puncture initial data for multi-black hole systems, and evolution strategies. Engage with Q&A sessions and discussions on constraint damping, providing a thorough understanding of this complex field in gravitational wave astrophysics.

Numerical relativity
How to simulate coalescing binary black holes?
Gravitational waves
Lecture plan
Numerical Relativity
Early & Brief History
2005 - Pretorius
Components of NR
Goal of NR
Projection into
Differential geometry w / in
Extrinsic curvature:
Adopted coordinates
Can also show
Further, all spatial objects objects collapse to 3 -D ones
Decomposing curvature & E. Egs.
Comments
Basics of Partial Difference Equation
Solving Constraints
Conformal trato
Side remark
Solved by e.g
BH momentum of spin : Transverse- traceless decomp of Kip
"Puncture initial data multi - BH boosted spinning BHS.
Evolutions -Strategies to modify equations
BSSN equations
Q&A
Note
Constraint damping
Q&A