Exact time-dependent states for throat quantized toroidal AdS black holes

We investigate exact non-stationary quantum states of vacuum toroidal black holes with a negative cosmological constant in arbitrary dimensions using the framework of throat quantization pioneered by Louko and Makela for Schwarzschild black holes. The system is equivalent to a harmonic oscillator on the half line, in which the central singularity is resolved quantum mechanically by imposing suitable boundary conditions that preserve unitarity. We identify two suitable families of exact time-dependent wave functions with Dirichlet or Neumann boundary conditions at the location of the classical singularity. We find that for highly non-stationary states of large-mass black holes, quantum fluctuations are not negligible in one family, while they are greatly suppressed in the other. The latter, therefore, may provide candidates for describing the dynamics of semi-classical black holes.

Smooth and sharp creation of a pointlike source for a $(3+1)$-dimensional quantum field

We analyse the smooth and sharp creation of a pointlike source for a quantised massless scalar field in $(3+1)$-dimensional Minkowski spacetime, as a model for the breakdown of correlations that has been proposed to occur at the horizon of an evaporating black hole. The creation is implemented by a time-dependent self-adjointness parameter at the excised spatial origin. In a smooth creation, the renormalised energy density $langle T_{00} rangle$ is well defined away from the source, but it is unbounded both above and below: the outgoing pulse contains an infinite negative energy, while a cloud of infinite positive energy lingers near the fully-formed source. In the sharp creation limit, $langle T_{00} rangle$ diverges everywhere in the timelike future of the creation event, and so does the response of an Unruh-DeWitt detector that operates in the timelike future of the creation event. The source creation is significantly more singular than the corresponding process in $1+1$ dimensions, analysed previously, and it may be sufficiently singular to break quantum correlations as proposed in a black hole spacetime.

The central role of symmetry in physics

Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the conjecture that symmetries may help us to one day uncover the ultimate theory that provides a unique, unified description of all observed physical phenomena. We examine some of the strengths and weaknesses of this conjecture.

New 2D dilaton gravity for nonsingular black holes

We construct a two-dimensional action that is an extension of spherically symmetric Einstein-Lanczos-Lovelock 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 Birkhoffs theorem. In complete analogy with spherically symmetric Einstein-Lanczos-Lovelock 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.

Designer black holes from new 2D gravity

We present a family of extensions of spherically symmetric Einstein-Lanczos-Lovelock gravity. The field equations are second order and obey a generalized Birkhoffs 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.

Two Dimensional Gravity as a modified Yang-Mills Theory

We study a deSitter/Anti-deSitter/Poincare Yang-Mills theory of gravity in d-space-time dimensions in an attempt to retain the best features of both general relativity and Yang-Mills theory: quadratic curvature, dimensionless coupling and background independence. We derive the equations of motion for Lie algebra valued scalars and show that in the geometric optics limit they traverse geodesics with respect to the Lorentzian geometry determined by the frame fields. Mixing between components appears to next to leading order in the WKB approximation. We then restrict to two space-time dimensions for simplicity, in which case the theory reduces to the well known Katanaev-Volovich model. We complete the Hamiltonian analysis of the vacuum theory and use it to prove a generalized Birkhoff theorem. There are two classes of solutions: with torsion and without torsion. The former are parametrized by two constants of motion, have event horizons for certain ranges of the parameters and a curvature singularity. The latter yield a unique solution, up to diffeomorphisms, that describes a space constant curvature .

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.

Throat quantization of the Schwarzschild-Tangherlini(-AdS) Black Hole

Adopting the throat quantization pioneered by Louko and Makela, we derive the mass and area spectra for the Schwarzschild-Tangherlini black hole and its anti-de~Sitter (AdS) generalization in arbitrary dimensions. We obtain exact spectra in three special cases: the three-dimensional BTZ black hole, toroidal black holes in any dimension, and five-dimensional Schwarzshild-Tangherlini(-AdS) black holes. For the remaining cases the spectra are obtained for large mass using the WKB approximation. For asymptotically flat black holes, the area/entropy has an equally spaced spectrum, as expected from previous work. In the asymptotically AdS case on the other hand, it is the mass spectrum that is equally spaced. Our exact results for the BTZ black hole with Dirichlet and Neumann boundary conditions are consistent with the spacing of the spectra of the corresponding operators in the dual CFT.

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.