Critical phenomena in gravitational collapse
Lead Research Organisation:
University of Southampton
Department Name: School of Mathematics
Abstract
Critical phenomena (scaling, self-similarity, and universality) occur in gravitational collapse for initial data that are close to the threshold between black-hole formation and dispersion. In particular, right at the threshold, naked singularities form. This has a bearing on cosmic censorship. The PhD project will initially focus on the toy model of the collapse of a rotating perfect fluid in 2+1 spacetime dimensions.
Organisations
People |
ORCID iD |
| Patrick Bourg (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/R513325/1 | 01/10/2018 | 30/09/2023 | |||
| 2127913 | Studentship | EP/R513325/1 | 01/10/2018 | 30/09/2021 | Patrick Bourg |
| Description | In critical collapse, one is interested in the phenomenology that occurs at the threshold of black-hole formation. Near the threshold, spacetime approaches, during an intermediary stage, a critical solution. In type II phenomena, the critical solution shrinks and the mass, charge and angular momentum of the black hole (for data that collapse) or the maximum of curvature (for data that disperse), scale as a power of distance to the black-hole threshold. For initial data right at the threshold, the initial data are driven neither to dispersion nor collapse. Instead, the fluid shrinks and the the density becomes larger and larger. This process continues so that arbitrary high density can be achieved. Unlike in a black hole, these large densities can be seen from far away. That is, they are not hidden inside an event horizon. The ensuing singularity that forms is said to be naked. In type I phenomena, the critical solution is static or time-periodic and the relevant quantity that scales is instead the lifetime of this metastable solution. The study of critical collapse marks an important milestone in numerical relativity and sheds some light into the weak and strong cosmic censorships. In particular, the self-similarity of the type II phenomena allows for arbitrary large curvature to be visible from null infinite. For this reason, critical collapse is also relevant to quantum gravity. Much of the current research on this topic revolves around understanding the effect of angular momentum. However, beyond spherical symmetry, the introduction of gravitational waves renders the dynamics substantially more difficult. As a toy model, I have analyzed the problem in 2+1 spacetime dimensions, where gravitational waves do not exist and, in axisymmetry, variables are still only functions of ``time'' and ``radius''. I have developed a completely new, fully constrained, high-resolution shock-capturing formulation of the Einstein-fluid equations in 2+1 dimensions in axisymmetry. The code is general enough that it can subsequently be extended to include other types of fluid. I have demonstrated convergence in the test cases of generic dispersion and collapse, and stable and unstable rotating stars. In the 2+1 dimensional case, I have found both type I and II phenomena, depending on the equation of the state. Interestingly, in the type II case, I have given strong numerical evidence that the critical solution can be approximated by an adiabatic sequence of stationary solutions whose size shrinks to zero exponentially. This result is unexpected and completely novel in the area of critical phenomena, challenges what is considered in the literature as one of the defining properties of the critical solution. Another surprising result is that the presence of angular momentum prevents the fluid to attain arbitrarily large densities, as it does in type II. Instead, as the fluid shrinks, it starts to rotated more and more rapidly. This creates some type of balancing that slows down the shrinking. We give strong evidence that the final end-state will not be a naked singularity. This gives further evidence in support of the weak cosmic censorship. |
| Exploitation Route | -) The outcome of this research show that some of the well-established properties of critical collapse turn out to be more subtle than what we thought. The different properties that we observed were also shown to be rather different to the case of a scalar field, which, to date, is the only other matter field that was investigated in 2+1 dimensions. This sheds further light onto the fact that the addition of angular momentum is quite non-trivial and it is difficult to predict a priori how different the ensuing phenomena will be compared to the case of non-rotation. -) The new code can be used as foundation for further studies, not only for critical collapse, but more generally gravitational collapsing scenarios. -) 2+1 spacetime dimensions is, in many ways, quite different from the usual 3+1 scenario. For one, it serves as an excellent testing ground for quantum gravity. As a result, the rather peculiar result that were obtained in our research, as compared to their well-known 3+1 dimensional counterparts, can give subtle hints as to the nature of quantum gravity. -) Finally, for our research, it was necessary to work in a background spacetime that is anti-de Sitter, instead of asymptotically flat. As a result, the result of our research has implication towards the AdS/CFT correspondence. |
| Sectors | Education,Other |