Tim Taves

We construct a two-dimensional action that is an extension of spherically symmetric Einstein–Lanczos–Lovelock (ELL) gravity. The action contains arbitrary functions of the areal radius and the norm squared of its gradient, but the field equations are second order and obey Birkhoff’s theorem. In complete analogy with spherically symmetric ELL gravity, the field equations admit the generalized Misner–Sharp mass as the first integral that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of interesting nonsingular black hole spacetimes than previously available.

We present a family of extensions of spherically symmetric Einstein-Lanczos-Lovelock gravity. The field equations are second order and obey a generalized Birkhoff's theorem. The Hamiltonian constraint can be written in terms of a generalized Misner-Sharp mass function that determines the form of the vacuum solution. The action can be designed to yield interesting non-singular black-hole spacetimes as the unique vacuum solutions, including the Hayward black hole as well as a completely new one. The new theories therefore provide a consistent starting point for studying the formation and evaporation of non-singular black holes as a possible resolution to the black hole information loss conundrum.

We present a model for studying the formation and evaporation of nonsingular (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 backreaction. 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.

Einstein-Gauss-Bonnet gravity provides a natural higher dimensional and higher order curvature generalization of Einstein gravity. It contains a new, presumably microscopic, length scale that should affect short distance properties of the dynamics, such as Choptuik scaling. We present the results of a numerical analysis in generalized flat slice coordinates of self-gravitating massless scalar spherical collapse in five and six dimensional Einstein-Gauss-Bonnet gravity near the threshold of black hole formation. Remarkably, the behavior is universal (i.e., independent of initial data) but qualitatively different in five and six dimensions. In five dimensions there is a minimum horizon radius, suggestive of a first order transition between black hole and dispersive initial data. In six dimensions no radius gap is evident. Instead, below the Gauss-Bonnet scale there is a change in the critical exponent and echoing period.

We derive the Hamiltonian for spherically symmetric Lovelock gravity using the geometrodynamics approach pioneered by Kucha\v{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.