scholarly journals A gauge-theoretic approach to gravity

2012 ◽  
Vol 468 (2144) ◽  
pp. 2129-2173 ◽  
Author(s):  
Kirill Krasnov
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Dynamical Theory ◽  
Uniqueness Theorems ◽  
Theoretic Approach ◽  
Field Equations ◽  
Yang Mills ◽  
Massless Spin ◽  
Invariant Gauge ◽  
Einstein’S General Relativity

Einstein's general relativity (GR) is a dynamical theory of the space–time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full nonlinear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an infinite-parameter class of gravity theories all describing just two propagating polarizations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang–Mills arise as sectors of a general diffeomorphism-invariant gauge theory. We finish by outlining a possible scenario of the ultraviolet completion of quantum gravity within this approach.

scholarly journals SECOND ORDER FORMALISM IN POINCARÉ GAUGE THEORY

2007 ◽  
Vol 16 (04) ◽  
pp. 655-679 ◽  
Author(s):  
M. LECLERC
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Type Equation ◽  
Approximate Solutions ◽  
Higher Order ◽  
Second Order ◽  
Field Equations ◽  
Tetrad Field ◽  
Yang Mills ◽  
Source Current

Changing the set of independent variables of Poincaré gauge theory and considering, in a manner similar to the second-order formalism of general relativity, the Riemannian part of the Lorentz connection as a function of the tetrad field, we construct theories that do not contain second or higher order derivatives in the field variables, possess a full general relativity limit in the absence of spinning matter fields, and allow for propagating torsion fields in the general case, the spin density playing the role of the source current in a Yang–Mills type equation for the torsion. The equivalence of the second-order and conventional first-order formalism is established and the corresponding Noether identities are discussed. Finally, a concrete Lagrangian is constructed and by means of a Yasskin-type ansatz, the field equations are reduced to a conventional Einstein–Proca system. Neglecting higher order terms in the spin-tensor, approximate solutions describing the exterior of a spin-polarized neutron star are presented and the possibility of the experimental detection of the torsion fields is briefly discussed.

scholarly journals ABELIAN DECOMPOSITION OF GENERAL RELATIVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3327-3341 ◽  
Author(s):  
Y. M. CHO
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Quantum Gravity ◽  
Lorentz Group ◽  
Lorentz Invariance ◽  
Gauge Potential ◽  
Abelian Decomposition ◽  
Gravitational Source ◽  
Einstein’S General Relativity ◽  
Local Lorentz Invariance

We present an Abelian decomposition of Einstein's general relativity, viewing Einstein's theory as a gauge theory of Lorentz group and identifying the gravitational connection as the gauge potential of Lorentz group. The decomposition confirms the existence of the restricted gravity which is much simpler than Einstein's theory but which has the full local Lorentz invariance (and thus the full general invariance). Moreover, it tells that Einstein's theory can be viewed as the restricted gravity which has the Lorentz covariant valence connection as the gravitational source. With the Abelian decomposition we show how to construct all possible vacuum gravitational connections, which can be classified by the knot topology π3(S3) = π3(S2). We discuss the physical implications of our result in quantum gravity.

scholarly journals Torsion Wave Solutions in Yang-Mielke Theory of Gravity

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Vedad Pasic ◽  
Elvis Barakovic
Keyword(s):  
General Relativity ◽  
Affine Connection ◽  
Future Research ◽  
Yang Mills ◽  
Axial Torsion ◽  
Wave Solutions ◽  
Torsion Wave ◽  
Theory Of Gravity ◽  
Affine Gravity ◽  
Einstein’S General Relativity

The approach of metric-affine gravity initially distinguishes it from Einstein’s general relativity. Using an independent affine connection produces a theory with 10 + 64 unknowns. We write down the Yang-Mills action for the affine connection and produce the Yang-Mills equation and the so-called complementary Yang-Mills equation by independently varying with respect to the connection and the metric, respectively. We call this theory the Yang-Mielke theory of gravity. We construct explicit spacetimes with pp-metric and purely axial torsion and show that they represent a solution of Yang-Mills theory. Finally we compare these spacetimes to existing solutions of metric-affine gravity and present future research possibilities.

scholarly journals Metric-Affine Gauge Theory of Gravity: I. Fundamental Structure and Field Equations

1997 ◽  
Vol 06 (03) ◽  
pp. 263-303 ◽  
Author(s):  
Frank Gronwald
Keyword(s):  
Gauge Theory ◽  
Reference Frames ◽  
Classical Field Theory ◽  
Classical Field ◽  
Affine Group ◽  
Field Equations ◽  
Yang Mills ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity ◽  
Affine Gravity

We give a self-contained introduction into the metric–affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang–Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric–affine gravity. The results are put into the dynamical framework of a classical field theory. We derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of tranlations is explained in detail.

scholarly journals General Relativity with a Positive Cosmological Constant as a Gauge Theory.

2018 ◽  
Author(s):  
Marta Dudek ◽  
Janusz Garecki
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Cosmological Constant ◽  
Gauge Field ◽  
Geometrical Interpretation ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Positive Cosmological Constant

In the paper we show that the general relativity in recent Einstein-Palatini formulation is equivalent to a gauge field. We begin with a bit of information of the Einstein-Palatini formulation and derive Einstein field equations from it. In the next section, we consider general relativity with a positive cosmological constant in terms of the corrected curvature. We show that in terms of the corrected curvature general relativity takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature.

scholarly journals THERMODYNAMICS OF EVOLVING LORENTZIAN WORMHOLES AT APPARENT HORIZON IN f(R) THEORY OF GRAVITY

2012 ◽  
Vol 27 (38) ◽  
pp. 1250220 ◽  
Author(s):  
H. SAIEDI
Keyword(s):  
General Relativity ◽  
Thermodynamic Properties ◽  
Apparent Horizon ◽  
Additional Term ◽  
Similar Form ◽  
Field Equations ◽  
Radiation Background ◽  
Theory Of Gravity ◽  
Einstein’S General Relativity

In the context of modified f(R) gravity, we attempt to study the thermodynamic properties of the evolving Lorentzian wormholes at the apparent horizon. It is shown that the wormhole can be derived from a particular f(R) model in the radiation background. Moreover, it has been shown that the field equations can be cast to a similar form [Formula: see text] at the apparent horizon for the evolving Lorentzian wormhole. Compared to the case of Einstein's general relativity, an additional term [Formula: see text] appears here.

STRING FIELD THEORY

1987 ◽  
Vol 02 (01) ◽  
pp. 1-76 ◽  
Author(s):  
MICHIO KAKU
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Gauge Theory ◽  
String Field Theory ◽  
Dimensional Space ◽  
Classical Solutions ◽  
Unified Field Theory ◽  
Superstring Theory ◽  
Yang Mills ◽  
Geometric Formulation

String theory has emerged as the leading candidate for a unified field theory of all known forces. However, it is impossible to trust the various phenomenological predictions of superstring theory based on classical solutions alone. It appears that the crucial problem of the theory, breaking ten dimensional space-time down to four dimensions, must be solved nonperturbatively before we can extract reliable predictions. String field theory may be the only formalism in which we can resolve this decisive question. Only a rigorous calculation of the true vacuum of the theory will determine which of the many classical solutions the theory actually predicts. In this review article, we summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. We also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group we call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU (N). Thus, the geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge theory.

scholarly journals Einstein gravity as a gauge theory for the conformal group

2021 ◽  
Author(s):  
Yannick Herfray ◽  
Carlos Scarinci
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Principal Bundle ◽  
A Priori ◽  
Conformal Group ◽  
Standard Theory ◽  
Field Equations ◽  
First Order ◽  
Torsion Freeness ◽  
Soldering Form

Abstract General Relativity in dimension $n = p + q$ can be formulated as a gauge theory for the conformal group $\SO\left(p+1,q+1\right)$, along with an additional field reducing the structure group down to the Poincaré group $\ISO\left(p,q\right)$. In this paper, we propose a new variational principle for Einstein geometry which realizes this fact. Importantly, as opposed to previous treatments in the literature, our action functional gives first order field equations and does not require supplementary constraints on gauge fields, such as torsion-freeness. Our approach is based on the ``first order formulation'' of conformal tractor geometry. Accordingly, it provides a straightforward variational derivation of the tractor version of the Einstein equation. To achieve this, we review the standard theory of tractor geometry with a gauge theory perspective, defining the tractor bundle a priori in terms of an abstract principal bundle and providing an identification with the standard conformal tractor bundle via a dynamical soldering form. This can also be seen as a generalization of the so called Cartan-Palatini formulation of General Relativity in which the ``internal'' orthogonal group $\SO\left(p,q\right)$ is extended to an appropriate parabolic subgroup $P\subset\SO\left(p+1,q+1\right)$ of the conformal group.

ON TIME DISLOCATION SOLUTION OF EINSTEIN FIELD EQUATIONS

1999 ◽  
Vol 14 (02) ◽  
pp. 93-97 ◽  
Author(s):  
L. C. GARCIA DE ANDRADE
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
External Solution ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Birkhoff Theorem ◽  
The Core ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity

The theory considered here is not Einstein general relativity, but is a Poincaré type gauge theory of gravity, therefore the Birkhoff theorem is not applied and the external solution is not vacuum spherically symmetric and tachyons may exist outside the core defect.

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