Jack Gegenberg

University of New Brunswick · Department of Mathematics and Statistics

We demonstrate that Huygens’ principle for gravitational waves fails in quadratic gravity models that exhibit conformal symmetry at high energies. This results in the blurring of gravitational wave signals over finite timescales related to the energy scale of new physics $M_{\star}$ . Furthermore, on very small scales the gravitational wave Green’s...

We study the quantum mechanics of self-gravitating thin shell collapse by solving the polymerized Wheeler-DeWitt equation. We obtain the energy spectrum and solve the time dependent equation using numerics. In contradistinction to the continuum theory, we are able to consistently quantize the theory for super-Planckian black holes, and find two cho...

We examine the cosmological sector of a gauge theory of gravity based on the SO(4,2) conformal group of Minkowski space. We allow for conventional matter coupled to the spacetime metric as well as matter coupled to the field that gauges special conformal transformations. An effective cosmological constant is generated dynamically via solution of th...

Beginning from canonical general relativity written in terms of Ashtekar variables, we derive a discrete phase space with a physical Hamiltonian for gravity. The key idea is to define the gravitational fields within a complex of three-dimensional cells such that the dynamics is completely described by discrete boundary variables, and the full theor...

We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2) and the action is of the Yang-Mills form, quadratic in the curvature. The resulting gravitational theory exhibits local conformal symmetry and reduces to Weyl-squared gravity under certain conditions. When the theory is linearized about flat spacetime, w...

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...

We study a type of modified bosonic string theory that has a scalar field with unit gradient ("dust") on the string worldsheet. The Hamiltonian analysis reveals a time reparametrization constraint that is linear in the dust field momentum. This suggests a natural "dust time" gauge. We give a Fock quantization of the theory in this gauge. The result...

We study a type of geometric theory with a non-dynamical one-form field. For a manifold that is $\mathbb{R}^4$, this is equivalent to a theory formulated on a symplectic manifold. Its dynamical variables are an $su(2)$ gauge field and a triad of $su(2)$ valued one-forms. Hamiltonian decomposition reveals that the theory has a true Hamiltonian, toge...

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of c...

Recently a {\it local} true (completely gauge fixed) Hamiltonian for spherically symmetric collapse was derived in terms of Ashtekar variables. We show that such a local Hamiltonian follows directly from the geometrodynamics of gravity theories that obey a Birkhoff theorem and possess a mass function that is constant on the constraint surface in va...

It is shown that the bosonic non-linear sigma model with torsion may be reinterpreted as a non-linear sigma model formulated on an algebraically extended two-dimensional worldsheet. The torsion term arises naturally as a consequence of the extended geometry. The two models, while locally equivalent, have distinct global features.

We study the homogeneous sector of the RST model describing the gravitational dynamics, including back-reaction, of radiating 2-d black holes. We find the exact solutions both in conformal gauge and in time-parametrized form, isolate the black hole sector of the classical phase space and quantize the near singularity dynamics in conformal gauge. We...

Simple cosmologies are constructed from solutions of the five-dimensional Einstein equations with a real, massless, non-self-interacting scalar-field source. It is demonstrated that nontrivial cosmological models occur only if the metric of the homogeneous and isotropic 3-space of the universe has nonpositive constant curvature. For the case of fla...

We analyze the $\delta=2$ Tomimatsu-Sato spacetime in the context of the proposed Kerr/CFT correspondence. This 4-dimensional vacuum spacetime is asymptotically flat and has a well-defined ADM mass and angular momentum, but also involves several exotic features including a naked ring singularity, and two disjoint Killing horizons separated by a reg...

Dimensionally reduced spherically symmetric gravity and its generalization, generic 2-D dilaton gravity, provide ideal theoretical laboratories for the study of black hole quantum mechanics and thermodynamics. They are sufficiently simple to be tractable but contain enough structure to allow the study of many deep issues in quantum gravity, such as...

We derive a partially gauge fixed Hamiltonian for black hole formation via real scalar field collapse. The class of models considered includes many theories of physical interest, including spherically symmetric black holes in $D$ spacetime dimensions. The boundary and gauge fixing conditions are chosen to be consistent with generalized Painleve-Gul...

We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one at each spatial point. The corresponding operator at each point is the product of the outgoing and ingoing nu...

We examine the fixed points to first-order RG flow of a non-linear sigma model with background metric, dilaton and tachyon fields. We show that on compact target spaces, the existence of fixed points with non-zero tachyon is linked to the sign of the second derivative of the tachyon potential $V''(T)$ (this is the analogue of a result of Bourguigno...

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing...

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing...

We implement a suggestion by Bakas and consider the Ricci flow of 3-d manifolds with one Killing vector by dimensional reduction to the corresponding flow of a 2-d manifold plus scalar (dilaton) field. By suitably modifying the flow equations in order to make them manifestly parabolic, we are able to show that the equations for the 2-d geometry can...

We derive general conditions under which geodesics of stationary spacetimes resemble trajectories of charged particles in an electromagnetic field. For large curvatures (analogous to strong magnetic fields), the quantum mechanicical states of these particles are confined to gravitational analogs of lowest Landau levels. Furthermore, there is an eff...

We derive general conditions under which geodesics of stationary spacetimes resemble trajectories of charged particles in an electromagnetic field. For large curvatures (analogous to strong magnetic fields), the quantum mechanicical states of these particles are confined to gravitational analogs of lowest Landau levels. Furthermore, there is an eff...

We present a string-inspired three-dimensional (3D) Euclidean field theory as the starting point for a modified Ricci flow analysis of the Thurston conjecture. In addition to the metric, the theory contains a dilaton, an antisymmetric tensor field and a Maxwell–Chern–Simons field. For constant dilaton, the theory appears to obey a Birkhoff theorem...

Three-dimensional gravity with a minimally coupled self-interacting scalar is considered. The fall-off of the fields at infinity is assumed to be slower than that of a localized distribution of matter, so that the asymptotic symmetry group is the conformal group. The counterterm Lagrangian needed to render the action finite is found by demanding th...

All but one of the three-dimensional Thurston geometries can be expressed as N2 × S1 or as a U(1) bundle over N2, where N2 denotes a two-dimensional Riemannian space of constant curvature. In an M-theoretic framework, these Thurston geometries can be related by Hopf T-duality. The exceptional case is the 'Sol geometry', which results from the dimen...

We describe a class of asymptotically AdS scalar field spacetimes, and calculate the associated conserved charges for three, four and five spacetime dimensions using the conformal and counterterm prescriptions. The energy associated with the solutions in each case is proportional to √M2-k2, where M is a constant and k is a scalar charge. In five sp...

We investigate thermodynamic properties of two types of asymptotically anti-de Sitter spacetimes: black holes and singular scalar field spacetimes. We describe the possibility that thermodynamic phase transitions can transform one spacetime into another, suggesting that black holes can radiate to naked singularities. Comment: 5 pages, Essay for 200...

We review the relevance to the black hole entropy problem of boundary dynamics in Chern-Simons gravity. We then describe a recent derivation of the action induced on the four dimensional boundary in a five dimensional Chern-Simons gravity theory with gauge invariant, anti-deSitter boundary conditions.

A sufficiently massive collapsing star will end its life as a spacetime singularity. The nature of the Hawking radiation emitted during collapse depends critically on whether the star's boundary conditions are such as would lead to the eventual formation of a black hole or, alternatively, to the formation of a naked singularity. This latter possibi...

We examine the dynamics induced on the four dimensional boundary of a five dimensional anti-deSitter spacetime by the five dimensional Chern-Simons theory with gauge group the direct product of SO(4,2) with U(1). We show that, given boundary conditions compatible with the geometry of 5d AdS spacetime in the asymptotic region, the induced surface th...

We show that there exists an intriguing connection between black holes in Jackiw-Teitelboim dilation gravity and Euclidean sine-Gordon solitons. Our analysis exploits a well-known relationship between constant curvature metrics and sine-Gordon solitons to show that in a particular coordinate system, the Jackiw-Teitelboim action reduces precisely to...

We construct a topological field theory which, on the one hand, generalizes BF theories in that there is non-trivial coupling to `topological matter fields'; and, on the other, generalizes the three-dimensional model of Carlip and Gegenberg to arbitrary dimensional manifolds. Like the three dimensional model, the theory can be considered to describ...

In this paper we describe a Liouville gravity which is induced by a set of quantum fields (constituents) and represents a two-dimensional analog of Sakharov's induced gravity. The important feature of the considered theory is the presence of massless constituents which are responsible for the appearance of the induced Liouville field. The role of t...

The vacuum Einstein equations in (4+m+n) dimensions are displayed for a class of metrics obtained by the Kaluza-Klein geometrisation of the (4+m)-dimensional Einstein-Maxwell equations. Consistency problems are solved by requiring that the metric be one of two types. In both cases the field equations split into spacetime and internal field equation...

The relationship between N-soliton solutions to the Euclidean sine-Gordon equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is investigated, with emphasis on the important role played by the dilaton in determining the black hole geometry. We show how an N-soliton solution can be used to construct ``sine-Gordon'' coordinates f...

We consider a parabolic-like systems of differential equations involving geometrical quantities to examine uniformization theorems for two- and three-dimensional closed orientable manifolds. We find that in the two-dimensional case there is a simple gauge theoretic flow for a connection built from a Riemannian structure, and that the convergence of...

In the talk, the relationship between black holes in Jackiw-Teitelboim(JT) dilaton gravity and solitons in sine-Gordon field theory is described. The well-known connection between solutions of the sine-Gordon equation and constant curvature metrics is reviewed and expanded. In particular, it is shown that solutions to the dilaton field equations fo...

We explore the relationship between black holes in Jackiw-Teitelboim (JT) dilaton gravity and solitons in sine-Gordon field theory. Our analysis expands on the well known connection between solutions of the sine-Gordon equation and constant curvature metrics. In particular, we show that solutions to the dilaton field equations for a given metric in...

In several recent publications Carlip, as well as Balachandran, Chandar, and Momen, has proposed a statistical-mechanical interpretation for black hole entropy in terms of “would-be gauge” degrees of freedom that become dynamical on the boundary to spacetime. After critically discussing several routes for deriving a boundary action, we examine thei...

We propose a model for the geometry of a dynamical spherical shell in which the metric is asymptotically Schwarzschild, but deviates from Ricci-flatness in a finite neighbourhood of the shell. Hence, the geometry corresponds to a `hairy' black hole, with the hair originating on the shell. The metric is regular for an infalling shell, but it bifurca...

A three-dimensional supergravity theory which generalizes the super IG theory of E. Witten [Topology-changing amplitudes in 2+1-dimensional gravity, Nuclear Physics B, Particle Physics B 323, No. 1, 113-140 (1989)] and resembles the model discussed recently by R. Mann and G. Papadopoulos [Killing spinors, the adS black hole and I(ISO(2,1)) gravity,...

A three dimensional supergravity theory which generalizes the super IG theory of Witten and resembles the model discussed recently by Mann and Papadopoulos is displayed. The partition function is computed, and is shown to be a three-manifold invariant generalizing the Casson invariant.

We calculate the statistical mechanical entropy associated with boundary terms in the two-dimensional Euclidean black holes in deSitter gravity.

We consider the most general dilaton gravity theory in 1+1 dimensions. By suitably parametrizing the metric and scalar field we find a simple expression that relates the energy of a generic solution to the magnitude of the corresponding Killing vector. In theories that admit black hole solutions, this relationship leads directly to an expression fo...

A unified description is presented of the physical observables and thermodynamic variables associated with black hole solutions in generic 2-D dilaton gravity. The Dirac quantization of these theories is reviewed and an intriguing relationship between the entropy of the black hole and the WKB phase of the corresponding physical wave functionals is...

We investigate the black hole solution to (2+1)-dimensional gravity coupled to topological matter, with a vanishing cosmological constant. We calculate the total energy, angular momentum and entropy of the black hole in this model and compare with results obtained in Einstein gravity. We find that the theory with topological matter reverses the ide...

The most general dilaton gravity theory in 2 spacetime dimensions is considered. A Hamiltonian analysis is performed and the reduced phase space, which is two dimensional, is explicitly constructed in a suitable parametrization of the fields. The theory is then quantized via the Dirac method in a functional Schrödinger representation. The quantum c...

The Dirac quantization of a 2+1 dimensional bubble is performed. The bubble consists of a string forming a boundary between two regions of space-time with distinct geometries. The ADM constraints are solved and the coupling to the string is introduced through the boundary conditions. The wave functional is obtained and the quantum uncertainty in th...

It is well known that one can parameterize 2-D Riemannian structures by conformal transformations and diffeomorphisms of fiducial constant curvature geometries; and that this construction has a natural setting in general relativity theory in 2-D. I will show that a similar parameterization exists for 3-D Riemannian structures, with the conformal tr...

We examine the relationship between covariant and canonical (Ashtekar/Rovelli/Smolin) loop variables in the context of BF type topological field theories in 2+1 and 3+1 dimensions, with respective gauge groups SO(2,1) and SO(3,1). The latter model can be considered as the simplest topological gravity theory in 3+1 dimensions. We carry out the canon...

A solvable two-dimensional conformally invariant midisuperspace model for black holes is obtained by imposing spherical symmetry in four-dimensional conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the theory is solved exactly to obtain the unique quantum wave functional for an isolated black hole with a fixed mass. By suitab...

We use a Hodge decomposition and its generalization to non-abelian flat vector bundles to calculate the partition function for abelian and non- abelian BF theories in $n$ dimensions. This enables us to provide a simple proof that the partition function is related to the Ray-Singer torsion defined on flat vector bundles for all odd-dimensional manif...

We study topological matter minimally coupled to gravity in 2+1 dimensions. We show that the resulting system has a finite dimensional physical phase space that can be exactly quantized. The model exhibits the mixing of “gravity” and “matter” degrees of freedom, and the impossibility of treating them independently.

We study topological matter minimally coupled to gravity in 2+1 dimensions. We show that the resulting system has a finite-dimensional physical phase space that can be exactly quantized. The model exhibits the mixing of ``gravity'' and ``matter'' degrees of freedom, and the impossibility of treating them independently.

2 + 1 gravity coupled to a scalar and antisymmetric tensor gauge field is examined. The quantum theory is finite-dimensional and exactly solvable, containing two phase space degrees of freedom in addition to those in the vacuum theory.

The theory of a scalar field conformally coupled to four dimensional Einsten gravity is dimensionally reduced to yield a conformally invariant two dimensional sigma model. The conformal anomaly, one-loop renormalized effective action and renormalized vacuum expectation value of the two dimensional stress-energy tensor are computed in a semi-classic...

The Weyl anomaly is computed for a class of two-dimensional algebraically extended bosonic sigma models. Although these models are classically equivalent to the standard bosonic sigma models with torsion, it is shown that they differ radically at the quantum level. In particular, a reasonable choice for the one-loop partition function for the algeb...

The route from string theory to a ten-dimensional supergravity/super-Yang-Mills field theory is briefly illumined. The process of extracting a classical four-dimensional gravity theory from the ten-dimensional theory is discussed and a simple model containing gravity, electromagnetism, a dilaton field, and a Kalb-Ramond field is proposed. The equat...

A variety of two-dimensional theories of gravitation with and without torsion are considered. We discuss the invariance properties and geometrical structure of each. One such theory considered predicts nontrivial dynamics for the evolution of the two-dimensional spacetime. We obtain some exact solutions for this theory.

Currently the heterotic string theory offers the best hope for describing the gravidynamics of elementary particles. This paper explores the question of what sort of macroscopic gravity theory will likely emerge from string theory.

If the heterotic string theory is the correct “theory of everything,” then the physics of our world at energies much lower than 1019 Gev should be governed, to a good approximation, by an appropriately modified version of N = 1 supergravity in ten dimensions coupled to a supersymmetrie 1 2 E8 x E8 gauge field.1,2 In fact, there is reason to believe...

Simple cosmologies are constructed from solutions of the five-dimensional Einstein equations with a real massless non-self-interacting scalar field source. It is demonstrated that non-trivial cosmological models occur only if the metric of the homogeneous and isotropic three-space of the universe has non-positive constant curvature. For the case of...

The equations of motion for charged particles are derived from the geodesic hypothesis in the five-dimensional Kaluza-Klein theory. It is shown that even within this purely classical framework the theory does not describe low mass charged particles, and that in the background of a Kaluza-Klein monopole, the long range scalr field has striking obser...

Riemannian space-times with self-dual curvature and which admit at least one Killing vector field (stationary) are examined. Such space-times can be classified according to whether a certain scalar field (which is the difference between the Newtonian and NUT potentials) reduces to a constant or not. In the former category (called here KSD) are the...

The Einstein–Maxwell–Klein–Gordon equations are simplified by imposing stationarity, isometric motion, the Weyl–Majumdar–Papapetrou condition, and axial symmetry. An exact (nonstatic) stationary solution is found such that the electric field vanishes, the magnetic field is constant and parallel to the polar axis, and the wavefunction of the matter...

An explicit proof is constructed to show that the field equations for a symmetric tensor fieldh ab describing massless spin-2 particles in Minkowski space-time are not covariant under the 15-parameter groupSO 4,2; this group is usually associated with conformal transformations on flat space, and here it will be considered as aglobal gauge group whi...

2+1 gravity coupled to a scalar and anti-symmetric tensor gauge field is examined. The quantum theory is finite-dimensional and exactly solvable, containing two phase space degrees of freedom in addition to those in the vacuum theory.

A number of recent results from an investigation of non-Riemannian geometries in two spacetime dimensions are described. The authors have discovered a fully geometric dynamical theory of 1+1 classical gravity; and have constructed a variety of solutions. The usual bosonic sigma model on a 1+1 dimensional base space and N dimensional target space (b...