Gravitational collapse of thin shells in equal angular momenta spacetimes
I have conducted a comprehensive investigation of the collapse of rotating shells onto black holes, with a large set of tuneable parameters: the mass of the shell, its spin and radial velocity at infinity, the dimensionality of spacetime D, and equation-of-state parameters characterising the imperfect fluid that makes up the shell. An extensive scan of the parameter space has been performed for D=5,7,9,11 and with fluids described by a linear equation-of-state. For pressureless fluids, i.e. dust shells, that start off from rest at infinity our results do not show any violation of cosmic censorship during the collapse of such equal angular momenta thin shells: If the shell plunges past the (preexistent) horizon one always gets another black hole. The only way a (overspinning) naked singularity is formed is if standard energy conditions are violated by the matter. Not even endowing the shells with tension or with large radial boosts at infinity allows the formation of naked singularities.
Exploring regular sources for EAM black hole exteriors
I accomplished an explicit construction of rotating solutions of the 5D Einstein equations sourced by imperfect fluids, with constant energy density and with anisotropic pressures and heat flux. The construction employs a Kerr-Schild ansatz and the equal angular momenta assumption. The solutions are asymptotically de Sitter but matching them onto a vacuum rotating exterior (Myers-Perry geometry) faces some obstacles. Thus, the attempt fell short of producing satisfactory exact solutions for rotating anisotropic stars. It may be possible to make progress by dropping the Kerr-Schild ansatz but the equations of motion must be solved numerically in this case. This is currently under study.
Dynamics of gravitational collapse of multiple shells in confined spaces
This task goes beyond the scope of the original proposal but is closely related and uses similar techniques. The idea was to investigate the turbulent instability of AdS towards formation of a black hole with an extremely clean multiple-shell model, thus clarifying the physical mechanisms at play. This instability was recently discovered through investigations with a spherically symmetric scalar field. We have studied the evolution of a system of two concentric thin shells, interacting only gravitationally, in both a spherical reflecting cavity or in AdS. The results are encouraging, showing that this very simple model captures the essence of the problem of scalar field collapse in AdS. In particular, the two-shells model exhibits critical phenomena and chaotic behaviour, both of which are observed with scalar fields in AdS. This study confirms that the physical mechanism behind the instability toward black hole formation in AdS is the transfer of energy to shorter wavelength modes. Moreover, it also indicates how this cascade can be avoided, i.e. in what situations do small perturbations of AdS not lead to black hole formation.
