Working Thesis Title
A numerical implementation of the Friedrich-Nagy gauge.
Gravitational waves are ripples in space-time that propagate at the speed of light. Originally posited shortly after Einstein published his General Theory of Relativity in 1915, they were only recently directly detected by gravitational wave observatories, such as LIGO. They are generated by the acceleration of massive bodies such as black holes and neutron stars.
Einstein’s equations, which govern gravitational waves, are highly non-linear so it becomes difficult to analytically investigate them, one then turns to numerical solutions. Various formalisms, such as BSSN and ccZ4, have been developed for solving Einstein’s equations in this manner by splitting the equations into constraint and evolution equations. However, almost all formalisms represent gravitational waves as complicated expressions of different variables, making direct setting impossible.
Friedrich and Nagy were the first to present a well-posed initial boundary value problem formulation of the Einstein equations in 1999. This has only recently been numerically implemented due to its complexity. The aim of my project is to generalise the Friedrich-Nagy initial boundary value problem to a full 3+1 system and numerically investigate the self-interaction and collisions of gravitational waves.
Supervisors:
Primary Supervisor: Chris Stevens
Research interests
General relativity, numerical relativity
Academic history
- 2014-2018 Bachelor of Science in Mathematics, Quaid-i-Azam University, Pakistan
- 2018-2021 Masters of Science in Applied Mathematics, Quaid-i-Azam University, Pakistan
