Speaker
Description
Gravitational waves, first predicted by Albert Einstein in 1916, are ripples in spacetime that travel at the speed of light. They were only recently detected directly by observatories like LIGO and are generated when massive objects, such as black holes or neutron stars, collide. They are important because they can provide information that electromagnetic radiation from surrounding matter cannot. However, studying their non-linear behaviour is extremely limited due to the complexity of the Einstein field equations.
Most numerical studies of general relativity are based on an initial boundary value problem (IBVP) for the Einstein equations. Standard numerical formulations involve second spatial derivatives and do not give a well-posed treatment of the boundary. The first well-posed IBVP was introduced by Friedrich and Nagy in 1999. The Friedrich–Nagy formulation provides a first-order, symmetric-hyperbolic IBVP with a natural maximally dissipative boundary treatment, yet it has only been explored numerically in a few simple cases.
This talk discusses a numerical implementation of the Friedrich–Nagy IBVP aimed at exploring non-linear gravitational-wave behaviour. In this framework, gravitational waves can be generated directly through boundary conditions, rather than by solving complicated elliptic PDEs to introduce them through the initial data, making it a nicer approach for future numerical studies.
| Research Area | Mathematical and Numerical Relativity |
|---|