Costa Lambrinoudis: Proposed 449 project
Numerical study of instability of flat spacetime in a cavity
- Reproduce and perhaps extend recent calculations which study instabilities of wave equations and thus of the
spacetime itself, when the spacetime is truncated at some finite radius.
Outline of work to be done
- Get acquainted with finite difference techniques for time dependent partial differential equations in one space
- Complete a warm-up project studying the spherically-symmetric scattering and absorption of scalar radiation by a black hole
- Implement the equations of motion for a self-gravitating scalar field in spherical symmetry wih boundarry conditions
corresponding to an infinite domain. Make a crude study of critical behaviour in the model.
- Implement the equations of motion for a self-gravitating scalar field in spherical symmetry with boundary conditions
corresponding to a finite domain (cavity). Investigate stability in the model. As time permits, investigate the
recent claims of a new type of scaling behaviour at the threshold of black hole formation.
- M. Maliborski, Instability of Flat Space Enclosed in a Cavity [PDF]
- M. Maliborski, Dynamics of Nonlinear Waves on Bounded Domains [PDF] (PhD Thesis)
- P. Bizon and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space [PDF]
- R.-G. Cai et al, On the critical behaviour of gapped gravitational collapse in confined spacetime [PDF]
- Warm up problem. Project 1 of Graduate Summer School on General Relativistic Hydrodynamics
- Introductory finite differencing