Exterior calculus on the computer: The REDUCE-package EXCALC applied to general relativity and to the Poincaré gauge theory

1987 ◽  
Vol 19 (2) ◽  
pp. 197-218 ◽  
Author(s):  
Eberhard Schrüfer ◽  
Friedrich W. Hehl ◽  
J. Dermott McCrea
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Exterior Calculus

scholarly journals The Kerr-Schild double copy in Lifshitz spacetime

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Gökhan Alkaç ◽  
Mehmet Kemal Gümüş ◽  
Mustafa Tek
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Charge Density ◽  
Localized Source ◽  
Curvature Term ◽  
Constant Charge Density ◽  
Arbitrary Dimensions ◽  
Double Copy ◽  
Theory Solution ◽  
Constant Charge

Abstract The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwell’s theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we give a general formulation, where no simplifying assumption about the background metric is made, and show that the gauge theory source is affected by a curvature term that characterizes the deviation of the background spacetime from a constant curvature spacetime. We demonstrate this effect explicitly by studying gravitational solutions with non-zero cosmological constant. We show that, when the background is flat, the constant charge density filling all space in the gauge theory that has been observed in previous works is a consequence of this curvature term. As an example of a solution with a curved background, we study the Lifshitz black hole with two different matter couplings. The curvature of the background, i.e., the Lifshitz spacetime, again yields a constant charge density; however, unlike the previous examples, it is canceled by the contribution from the matter fields. For one of the matter couplings, there remains no additional non-localized source term, providing an example for a non-vacuum gravity solution corresponding to a vacuum gauge theory solution in arbitrary dimensions.

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

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 24
Author(s):  
Marta Dudek ◽  
Janusz Garecki
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Cosmological Constant ◽  
Gauge Field ◽  
Geometrical Interpretation ◽  
Positive Cosmological Constant ◽  
Four Dimensions ◽  
Action Integral ◽  
Fields Equations

In this paper, we show that the general relativity action (and Lagrangian) in recent Einstein–Palatini formulation is equivalent in four dimensions to the action (and Langrangian) of a gauge field. First, we briefly showcase the Einstein–Palatini (EP) action, and then we present how Einstein fields equations can be derived from it. In the next section, we study Einstein–Palatini action integral for general relativity with a positive cosmological constant Λ in terms of the corrected curvature Ω c o r . We see that in terms of Ω c o r this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω c o r .

scholarly journals GENERAL RELATIVITY AS A CONSTRAINED GAUGE THEORY

2006 ◽  
Vol 03 (08) ◽  
pp. 1493-1500 ◽  
Author(s):  
STEFANO VIGNOLO ◽  
ROBERTO CIANCI ◽  
DANILO BRUNO
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Hamiltonian Formulation

The formulation of General Relativity presented in [1] and the Hamiltonian formulation of Gauge theories described in [2] are made to interact. The resulting scheme allows to see General Relativity as a constrained Gauge theory.

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.

Reformulation of general relativity as a gauge theory

1977 ◽  
Vol 103 (1) ◽  
pp. 208-232 ◽  
Author(s):  
M Carmeli ◽  
S Malin
Keyword(s):  
General Relativity ◽  
Gauge Theory
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