Related papers: Plebanski Formulation of General Relativity: A Pra…
This thesis studies general relativity (GR) using chiral formulations, which take advantage of the decomposition of the four-dimensional Lorentz group into self-dual and anti-self-dual sectors. Within this framework, GR can be expressed…
The first order Plebanski formulation of (complex) general relativity (GR) in terms of self-dual 2-forms admits a generalization, proposed by Krasnov, that is qualitatively different from other possible generalizations of GR in terms of…
Plebanski's second heavenly equation reduces the problem of finding a self-dual Einstein metric to solving a non-linear second-order PDE for a single function. Plebanski's original equation is for self-dual metrics obtained as perturbations…
In Plebanski's self-dual formulation general relativity becomes SO(3) BF theory supplemented with the so-called simplicity (or metricity) constraints for the B-field. The main dynamical equation of the theory states that the curvature of…
I discuss the (2,2)-formalism of general relativity based on the (2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian signature. In this formalism general relativity is describable as a Yang-Mills gauge theory defined on…
We consider a certain theory of 3-forms in 7 dimensions, and study its dimensional reduction to 4D, compactifying the 7-dimensional manifold on the 3-sphere of a fixed radius. We show that the resulting 4D theory is General Relativity (GR)…
We present a theory of four-dimensional quantum gravity with massive gravitons which may be essentially renormalizable. In the Plebanski formulation of General Relativity (GR), in which the tetrads, the connection and the curvature are all…
A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski…
We revise the classical continuum formulation behind the Spin Foam approach to the quantization of gravity. Based on the recent applications of the current EPRL-FK model beyond triangulations, we identify the tension with the implementation…
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…
It is well known that, making the Abelian projection of Einstein's theory one can obtain the restricted gravity which is simpler than Einstein's theory but describes the core dynamics of Einstein's gravity. In this paper we present the…
We describe and study a certain class of modified gravity theories. Our starting point is Plebanski formulation of gravity in terms of a triple B^i of 2-forms, a connection A^i and a ``Lagrange multiplier'' field Psi^ij. The generalization…
Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution---the exact seven parameter solution of Pleba\'nski--Demia\'nski (PD)---to demonstrate these analogies for…
We present a basics of the Einstein General Theory of Relativity. In the first part of this review we derive relations of Riemann geometry which are used in the General Relativity. In the second part we discuss Einstein Equations and some…
We give a pedagogical introduction of the essential features of General Theory of Relativity (GTR) in the format of an undergraduate (UG) project. A set of simple MATHEMATICA code is developed which enables the UG students to calculate the…
The Plebanski formulation of complex general relativity is given in terms of variables valued in the complexification of the $so(3)$ Lie algebra. Therefore, it is genuinely a gauge theory that is also diffeomorphism-invariant. For this…
We present a new $BF$-type action for complex general relativity with or without a cosmological constant resembling Plebanski's action, which depends on an SO(3,$\mathbb{C}$) connection, a set of 2-forms, a symmetric matrix, and a 4-form.…
We present an alternative geometric inspired derivation of the quantum cosmology arising from a brane universe in the context of {\it geodetic gravity}. We set up the Regge-Teitelboim model to describe our universe, and we recover its…
An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian…
A pedagogical description of a simple ungeometrical approach to General Relativity is given, which follows the pattern of well understood field theories, such as electrodynamics. This leads quickly to most of the important weak field…