The Einstein Field Equations (EFE’s) are nonlinear, coupled, partial differential equations that describe the relation between the geometry of a region of spacetime and its matter/energy content. A severe complication is that, with the exception of a few idealised cases characterised by high degrees of symmetry, the EFE’s simply cannot be obtained analytically; we need a computer to do the heavy lifting for us. That being said, computers (for better or worse) lack a sense of humour; if you feed them nonsense, they will calculate nonsense. Therefore, in order to find solutions to realistic (asymmetric) spacetimes, we need to be able to somehow prescribe the right numerical recipe to the machine.This recipe comes in several different flavours (formalisms), the main ones being
- ADM (aka ADMY) formalism
- BSSN (aka BSSNOK) formalism
- Formulations of (covariant and) conformal Z4-like systems (e.g., Z4c & fCCZ4)
- Generalised Harmonic Coordinates with Constraint Damping (GHCD)
My main research interests lie in the study of asymmetric solutions to the EFE’s, using the full strength of numerical general relativity. At the moment, I am investigating cases that are relevant to theoretical cosmology (bubble nucleation & evolution). Other topics of interest are asymmetric solutions of Einstein-matter systems, as well as dynamics of compact objects (merger of black holes and neutron stars in binary systems).