Version Of Gravity Research Articles

Thinking about the Universe

This article is largely a review and critical analysis of earlier papers by the author, and, within the broad background of the literature on this subject, it discusses the problems in the early stages of evolution of the Universe close to the singularity point. Special attention is paid to analyzing the properties of the de Sitter and Friedmann universes, and discussing the physical conditions which could induce a transition from one type of universe to another. Various modifications of the usual Einstein equations are presented which could serve as the dynamical basis of such a transition. A version of gravity in which the gravitational constant is replaced by a function of the matter (energy) density approaching zero as the density increases to its maximum value is discussed in detail. The possible nontrivial role of black holes during the inflationary stage of development of the Universe and also (for closed universes) during the final collapse stage is discussed. The possibility that the physical laws change in regions of space of size close to the Planck length, which could lead to the existence of a special physics of the ultra-microscopic world, is especially emphasized.

The two-point function of c = −2 matter coupled to 2D quantum gravity

We construct a reparametrization invariant two-point function for c = −2 conformal matter coupled to two-dimensional quantum gravity. From the two-point function we extract the critical indices ν and η. The results support the quantum gravity version of Fissher's scaling relation. Our approach is based on the transfer matrix formalism and exploits the formulation of the c = −2 string as an O( n) model on a random lattice.

A new nested boundary condition for a primitive equation ocean model

Nested boundary techniques are developed based on the results of Perkins [1993] and Blake [1991]. We focus on the numerical and physical consistency needs across the nested boundary. These techniques replace the transition zone used by other researchers with a numerically and a physically based correction step. We demonstrate our method using a nested, reduced gravity version of the Naval Research Laboratory (NRL) primitive equation ocean model and a two‐layer hydrodynamic finite‐depth version of the same model. Numerical experiments are performed using integrations of both an idealized double gyre and a realistic Greenland Iceland Norwegian (GIN) Sea configuration. To illustrate the need for improved boundary treatment, we present a numerical study of boundary errors. The study illustrates the fragile nature of nested boundary conditions. With even small errors, a dramatic impact is observed on the formation (or lack thereof) of the Atlantic‐Norwegian Current, which is responsible for transporting North Atlantic water to the Arctic Ocean, in the GIN Sea configuration.

Quantizing Regge calculus

A discretized version of canonical gravity in (3 + 1) dimensions introduced in a previous paper is further developed, introducing the Liouville form and the Poisson brackets, and studying them in detail in an explicit parametrization that shows the nature of the variables when the second class constraints are imposed. It is then shown that, even leaving aside the difficult question of imposing the first class constraints on the states, it is impossible to quantize the model directly using complex variables and leaving the second class constraints to fix the metric of the quantum Hilbert, because one cannot find a metric which makes the area variables Hermitean.

A q-DEFORMED VERSION OF THE HEAVENLY EQUATIONS

Using a q-deformed Moyal algebra associated with the group of area-preserving diffeomorphisms of the two-dimensional torus T2, sdiffq(T2), a q-deformed version of the heavenly equations is given. In addition, the two-dimensional chiral version of self-dual gravity in this q-deformed context is briefly discussed.

Scaling in quantum gravity

The 2-point function is the natural object in quantum gravity for extracting critical behavior: The exponential falloff of the 2-point function with geodesic distance determines the fractal dimension dH of space-time. The integral of the 2-point function determines the entropy exponent γ, i.e. the fractal structure related to baby universes, while the short distance behavior of the 2-point function connects γ and dH by a quantum gravity version of Fisher's scaling relation. We verify this behavior in the case of 2d gravity by explicit calculation.

Gauge dependence in higher derivative quantum gravity and the conformal anomaly problem

We examine the gauge dependence in higher derivative quantum gravity and find that a change of gauge condition leads to a variation of the effective action that is proportional to the conformal shift of the classical action. From this follows that one can not explain the appearance of the nonconformal counterterms in the Weyl gravity as the effect of a “bad” gauge. The last claim is a serious reasoning in favour of the anomaly origin of Weyl gravity. Moreover we consider a new version of (induced) conformal gravity and find that the gauge dependence in this theory also has no relation to the existence of nonconformal divergencies.

Large N 2D Yang-Mills Theory and Topological String Theory

We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A=0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's ``\Omega^{-1} points.'' We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach.

Erratum: (2+1)-dimensional Chern-Simons gravity as a Dirac square root

For (2+1)-dimensional spacetimes with the spatial topology of a torus, the transformation between the Chern-Simons and ADM versions of quantum gravity is constructed explicitly, and the wave functions are compared. It is shown that Chern-Simons wave functions correspond to modular forms of weight 1/2, that is, spinors on the ADM moduli space, and that their evolution (in York's ``extrinsic time'' variable) is described by a Dirac equation. (This version replaces paper 9109006, which was garbled by my mailer.)

TOPOLOGICAL HALF-FLAT GRAVITY

A topological field theory modeling the moduli space of half-flat gravitational instantons is presented, in which the fundamental gravitional fields are a trio of self-dual two-forms and an SU(2) connection. The theory can be understand as a topological version of the (Euclidean) Einstein gravity.

The universe created from vacuum in the quantum-gravity interpretation of Brans-Dicke’s theory

A quantum gravity version is given to the Brans-Dicke theory. We find that the matter field quantum fluctuation induces the conformal quantum fluctuation of space-time and that the latter back-reacts to the classical space-time and transforms it from Einstein space-time into the Brans-Dicke one. Based on Brans-Dicke theory, we discuss the creation of universe from vacuum.

A classical model for the electron

The construction of classical and semi-classical models for the electron has had a long and distinguished history. Such models are useful more for what they teach us about field theory than what they teach us about the electron. In this Letter I exhibit a classical model of the electron consisting of ordinary electromagnetism coupled with a self-interacting version of Newtonian gravity. The gravitational binding energy of the system balances the electrostatic energy in such a manner that the total rest mass of the electron is finite.

Topological gravity

A version of conformal gravity is formulated with a local fermionic symmetry that is reminiscent of BRST invariance. It may have mathematical applications (gravitational counterpart of Donaldson theory) or physical ones (unbroken phase of general relativity).

Quantum-gravity interpretation of Brans-Cicke theory—the back-reaction of the vacuum matter field upon the Einstein space-time

A quantum gravity version is given to the Brans-Dicke theory. We find that the matter field quantum fluctuation induces the conformal quantum fluctuation of space-time, and that the latter backreacts to the classical space-time and transforms it from Einstein space-time into the Brans-Dicke one.

Goldstone Type (Non-Poincare) Supergravity

The gauge description of gravity as Higgs-Goldstone type fields is extended on supergravity. Following the Poincaré gauge version of gravity, contemporary supergravity models are connected with the super (graded) Poincaré group. Most of these models are based on gauge coodinate supertranslations in the spirit of Kibble’s gravity approach,1) although graded affine bundles come into play, too.2) However, Poincaré gauge versions of gravity (especially Kibble’s one criticized by F. Hehl and others) fail to be quite satisfactory.3),4) The Poincaré supergravity faces its own additional difficulties. For instance, many authors ignore the fact that by the supertraslation law coodinates Xµ are not real, but represent even elements of a Grassmann algebra. The Poincaré gauge versions of gravity lost sight of the fact that not only gauge potentials, but Higgs-Goldstone fields appear in a gauge theory when symmetries are spontaneously broken. Einstein’s gravitational field and supergravity turn out to be fields just of this type.

Super lattices and gauge theory.

There has been a fundamental flaw in all previous attempts to put supersymmetry on the lattice. Because supersymmetry closes on the Poincare group, and since the Wilson lattice breaks Poincare invariance, the standard lattice must necessarily break supersymmetry. We solve this difficulty by putting supersymmetry on a random super lattice, where each random site is a point in super space (x/sub i/,xi/sub i/). We construct the action out of unitary SU(N) superfields connecting two such super lattice sites and sum the traces over simplexes. The theory is manifestly supersymmetric because there is no preferred direction in either real or Grassmann space. This supersymmetric lattice gauge theory on a random lattice reduces to the usual supersymmetric gauge theory in the continuum limit. We discuss applications, such as calculating nonperturbative corrections to the vacuum energy, which may yield a large enough supersymmetry breaking to explain the hierarchy problem. We discuss using random lattices to describe a lattice version of gravity and supergravity.

On a nonlinear and Lorentz-invariant verson of Newtonian gravitation

This paper gives a full nonlinear version of Newtonian gravity in which the gravitational energy acts as a source of the gravitational field. The generalized field equation for the scalar gravitational potential is solved for a spherically symmetric localized distribution of matter. It is shown that the perihelia of orbits of test particles in such a field precess steadily. The effect is, however, too small to account for the observed shift in the perihelion of planet Mercury. Further, the bending of light in this theory is zero. It is suggested that these inadequacies of the quasi-Newtonian framework call for more sophisticated approaches to gravity.

Matter field infinities in axial gauge gravity

The one-loop infinities for scalar, spinor and vector fields due to gravitational interactions are computed in the axial gravity gauge for the Einstein-Hilbert action. The results reveal an axis dependence, in addition to their expected non-renormalisability, which is expected to get progressively worse in higher orders of perturbation theory. This means that gauge equivalences between covariant and non-covariant gauges are impossible in ordinary quantum gravity (unlike renormalisable theories such as flavourdynamics or chromodynamics) unless cancellation of infinities occurs through some supersymmetric mechanism or unless a renormalisable conformal version of gravity is adopted.

Dynamical structure of linearizedGL(4) gravities

The physical content of the three more natural models ofGL(4) gravity is analyzed, for the case of weak fields. The first model we deal with is the linearized version of Yang's onetensor-field gravity. It is shown that this is a scalar-tensor theory, with its scalar part contained in the symmetric tensorh αν, instead of appearing explicitly, externally to the symmetric tensorh αν, as happens in Brans-Dicke type of scalar-tensor theories. The second and the third linearized models, which can both be derived from the fourth-order action postulated by Yang, turn out to be two-tensor decoupled systems. In both cases one of the tensors is the symmetric weak metric gravity tensor field. The second tensor appearing in these two models, representing theGL(4)-gauge field, is either a linearized symmetric affinity (in the second model) or a linearized but nonsymmetric affinity (for the third model). It is shown that in these last two cases the affinity contains a helicity-3 propagating field. The connection is also given between the fourth-order system which determines the dynamical structure (for the last two models) of the metric tensor and the third-order Yang model of gravity. Owing to the presence of helicity-3 fields we show that it is better to regard Yang's action as an action for a two-tensor system instead of trying to recover from it a pure gravity (one-tensor-field) action. Finally, it is shown what is the dynamical structure of the second and third linearized two-tensor models which can be derived from Yang's action.