# Costa Lambrinoudis: Proposed 449 project

Numerical study of instability of flat spacetime in a cavity

## Motivation

- 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
dimension
- 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.

## References

- 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]

## Resources

- Warm up problem. Project 1 of Graduate Summer School on General Relativistic Hydrodynamics
- Introductory finite differencing