Related papers: Instanton representation of Plebanski gravity. Euc…
This paper presents a self-contained introduction into the instanton representation of Plebanski gravity (IRPG), a GR formulation which uses a gauge connection and a three by three matrix as basic variables. In this paper we explore some…
We present a reformulation of general relativity as a `generalized' Yang--Mills theory of gravity, using a SO(3,C) gauge connection and the self-dual Weyl tensor as dynamical variables. This formulation uses Plebanski's theory as the…
Using the instanton representation method we construct a general solution for GR in the spatially homogeneous case restricted to diagonal variables. This paper provides a testing ground and physical intuition for many of the salient…
In this paper we quantize the Klein--Gordon scalar field coupled to gravity in the instanton representation for spatially homogeneous variables. The construction provides a well-defined Hilbert space of states for generic self-interaction…
Using the instanton representation method, we re-construct graviton solutions about DeSitter spacetime. We have used this example as a testing arena to expose the internal structure of the method and to establish that it works for known…
In this paper we illustrate the dynamics of the instanton representation in the description of vacuum GR in minisuperspace for undensitized variables. We uncover a new class of general solutions in both the degenerate and the nondegenerate…
In this paper we carry out a quantization of gravity coupled to massless spin 1/2 fermions through the instanton representation of Plebanski gravity. We have constructed a Hilbert space of states for this model, and we have computed the…
In this paper we examine the phase space structure of a noncanonical formulation of 4-dimensional gravity referred to as the Instanton representation of Plebanski gravity (IRPG). The typical Hamiltonian (symplectic) approach leads to an…
In this paper we show that the instanton representation of Plebanski gravity exhibits a Hilbert space of harmonic oscillator-like coherent states. We put in place the formalism and carry out the construction of the states, and we elucidate…
Physical properties of gravitational instantons which are derivable from minimal surfaces in 3-dimensional Euclidean space are examined using the Newman-Penrose formalism for Euclidean signature. The gravitational instanton that corresponds…
The instanton representation of Plebanski gravity provides as equations of motion a Hodge self-duality condition and a set of `generalized' Maxwell's equations, subject to gravitational degrees of freedom encoded in the initial value…
In this paper we apply the instanton representation method to the construction of spherically symmetric blackhole general relativity solutions. The instanton representation implies the existence of additional Type D solutions which are…
We study the Einstein-Chern-Simons gravity coupled to Yang-Mills-Higgs theory in three dimensional Euclidean space with cosmological constant. The classical equations reduce to Bogomol'nyi type first order equations in curved space. There…
Three dimensional Euclidean gravity in the dreibein-spin connection formalism is investigated. We use the monopole-instanton ansatz for the dreibein and the spin connection. The equations of motion are solved. We point out a two dimensional…
A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of…
We show that a certain action which gives rise to the pure spin connection formulation of gravity by CDJ can be consistently derived from the action for the instanton representation of Plebanski gravity. This is an illustrative example of…
In this paper we have constructed a Hilbert space of states solving the initial value constraints of GR in the instanton representation of Plebanski gravity. The states are labelled by two free functions of position constructed from the…
The instanton representation of Plebanski gravity admits a natural canonical structure where the (densitized) eigenvalues of the CDJ matrix are the basic momentum space variables. Canonically conjugate configuration variables exist for six…
We discuss four-dimensional "spatially homogeneous" gravitational instantons. These are self-dual solutions of Euclidean vacuum Einstein's equations with potentially non-vanishing cosmological constant. They are endowed with a product…
One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravity field is described by an elliptic Poisson equation. We…