Integrability of the Einstein-nonlinear $SU(2)$ $sigma$-model in a nontrivial topological sector

The integrability of the $Lambda-$Einstein-nonlinear $SU(2)$ $sigma$-model with nonvanishing cosmological charge is studied. We apply the method of singularity analysis of differential equations and we show that the equations for the gravitational field are integrable. The first few terms of the solution are presented.

Modelling the Evaporation of Non-singular Black Holes

We present a model for studying the formation and evaporation of non-singular (quantum corrected) black holes. The model is based on a generalized form of the dimensionally reduced, spherically symmetric Einstein--Hilbert action and includes a suitably generalized Polyakov action to provide a mechanism for radiation back-reaction. The equations of motion describing self-gravitating scalar field collapse are derived in local form both in null co--ordinates and in Painleve--Gullstrand (flat slice) co--ordinates. They provide the starting point for numerical studies of complete spacetimes containing dynamical horizons that bound a compact trapped region. Such spacetimes have been proposed in the past as solutions to the information loss problem because they possess neither an event horizon nor a singularity. Since the equations of motion in our model are derived from a diffeomorphism invariant action they preserve the constraint algebra and the resulting energy momentum tensor is manifestly conserved.

Hamiltonian dynamics of Lovelock black holes with spherical symmetry

We consider spherically symmetric black holes in generic Lovelock gravity. Using geometrodynamical variables we do a complete Hamiltonian analysis, including derivation of the super-Hamiltonian and super-momentum constraints and verification of suitable boundary conditions for asymptotically flat black holes. Our analysis leads to a remarkably simple fully reduced Hamiltonian for the vacuum gravitational sector that provides the starting point for the quantization of Lovelock block holes. Finally, we derive the completely reduced equations of motion for the collapse of a spherically symmetric charged, self-gravitating complex scalar field in generalized flat slice (Painlev{e}-Gullstrand) coordinates.

Geometrodynamics of spherically symmetric Lovelock gravity

We derive the Hamiltonian for spherically symmetric Lovelock gravity using the geometrodynamics approach pioneered by Kuchav{r} in the context of four-dimensional general relativity. When written in terms of the areal radius, the generalized Misner-Sharp mass and their conjugate momenta, the generic Lovelock action and Hamiltonian take on precisely the same simple forms as in general relativity. This result supports the interpretation of Lovelock gravity as the natural higher-dimensional extension of general relativity. It also provides an important first step towards the study of the quantum mechanics, Hamiltonian thermodynamics and formation of generic Lovelock black holes.