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 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 THE CONSISTENT NEWTONIAN LIMIT OF EINSTEIN'S GRAVITY WITH A COSMOLOGICAL CONSTANT

2001 ◽  
Vol 10 (05) ◽  
pp. 649-661 ◽  
Author(s):  
MAREK NOWAKOWSKI
Keyword(s):  
Boundary Condition ◽  
General Relativity ◽  
Cosmological Constant ◽  
Mass Distribution ◽  
Newtonian Limit ◽  
Spherically Symmetric ◽  
Maximum Mass ◽  
Finite Range ◽  
Positive Cosmological Constant ◽  
The Poisson Equation

We derive the "exact" Newtonian limit of general relativity with a positive cosmological constant Λ. We point out that in contrast to the case with Λ=0, the presence of a positive Λ in Einsteins's equations enforces, via the condition |Φ|≪1 on the potential Φ, a range ℛ max (Λ)≫r≫ℛ min (Λ), within which the Newtonian limit is valid. It also leads to the existence of a maximum mass, ℳ max (Λ). As a consequence we cannot put the boundary condition for the solution of the Poisson equation at infinity. A boundary condition suitably chosen now at a finite range will then get reflected in the solution of Φ provided the mass distribution is not spherically symmetric.

CONSISTENT QUANTIZATION OF A CHIRAL GAUGE THEORY IN FOUR DIMENSIONS

1989 ◽  
Vol 04 (27) ◽  
pp. 2675-2683 ◽  
Author(s):  
SHOGO MIYAKE ◽  
KEN-ICHI SHIZUYA
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Gauge Field ◽  
Current Algebra ◽  
Gauge Theories ◽  
Present Theory ◽  
Particle Spectrum ◽  
Four Dimensions ◽  
Symmetric Formulation

Using a gauge-symmetric formulation of anomalous gauge theories, we study the consistency and symmetry contents of a chiral gauge theory in four dimensions. The gauge symmetry, restored by the inclusion of the Wess-Zumino term, is spontaneously broken and the gauge field acquires a mass. Symmetry arguments are used to determine the particle spectrum and the current algebra of the model. Our analysis indicates that, apart from a question of renormalizability, the present theory is a consistent gauge theory.

DE SITTER GRAVITY AND SUPERGRAVITY IN THREE DIMENSIONS AS CHERN-SIMONS THEORIES

1990 ◽  
Vol 05 (12) ◽  
pp. 935-941 ◽  
Author(s):  
K. KOEHLER ◽  
F. MANSOURI ◽  
CENALO VAZ ◽  
L. WITTEN
Keyword(s):  
Gauge Theory ◽  
Cosmological Constant ◽  
Classical Theory ◽  
Three Dimensional ◽  
Three Dimensions ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Supergravity Theory ◽  
Gauge Transformations ◽  
Chern Simons

We construct a de Sitter supergravity theory in 2 + 1 dimensions as the Chern-Simons gauge theory of the supergroup OSp (1|2; C). The resulting action is a consistent classical supergravity theory with a positive cosmological constant. As in other three dimensional Chern-Simons theories, diffeomorphisms are shown to be equivalent to gauge transformations of OSp (1|2; C) on shell. Consistency of the corresponding classical theory is briefly discussed.

scholarly journals The shape of bouncing universes

2017 ◽  
Vol 26 (12) ◽  
pp. 1743016 ◽  
Author(s):  
John D. Barrow ◽  
Chandrima Ganguly
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Cosmological Constant ◽  
Inflexion Point ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Entropy Increase

What happens to the most general closed oscillating universes in general relativity? We sketch the development of interest in cyclic universes from the early work of Friedmann and Tolman to modern variations introduced by the presence of a cosmological constant. Then we show what happens in the cyclic evolution of the most general closed anisotropic universes provided by the Mixmaster universe. We show that in the presence of entropy increase its cycles grow in size and age, increasingly approaching flatness. But these cycles also grow increasingly anisotropic at their expansion maxima. If there is a positive cosmological constant, or dark energy, present then these oscillations always end and the last cycle evolves from an anisotropic inflexion point towards a de Sitter future of everlasting expansion.

scholarly journals Neutral signature gauged supergravity solutions

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
J. Gutowski ◽  
W. A. Sabra
Keyword(s):  
Cosmological Constant ◽  
Geometric Structure ◽  
Base Space ◽  
Killing Spinor ◽  
Positive Cosmological Constant ◽  
3 Dimensional

Abstract We classify all supersymmetric solutions of minimal D = 4 gauged supergravity with (2) signature and a positive cosmological constant which admit exactly one Killing spinor. This classification produces a geometric structure which is more general than that found for previous classifications of N = 2 supersymmetric solutions of this theory. We illustrate how the N = 2 solutions which consist of a fibration over a 3-dimensional Lorentzian Gauduchon-Tod base space can be written in terms of this more generic geometric structure.

scholarly journals Supersymmetric solitons and a degeneracy of solutions in AdS/CFT

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Andrés Anabalón ◽  
Simon F. Ross
Keyword(s):  
Phase Transition ◽  
Riemann Surface ◽  
Magnetic Flux ◽  
Gauge Field ◽  
Wilson Line ◽  
Saddle Points ◽  
Planar Boundary ◽  
Four Dimensions ◽  
Special Value

Abstract We study Lorentzian supersymmetric configurations in D = 4 and D = 5 gauged $$ \mathcal{N} $$ N = 2 supergravity. We show that there are smooth 1/2 BPS solutions which are asymptotically AdS4 and AdS5 with a planar boundary, a compact spacelike direction and with a Wilson line on that circle. There are solitons where the S1 shrinks smoothly to zero in the interior, with a magnetic flux through the circle determined by the Wilson line, which are AdS analogues of the Melvin fluxtube. There is also a solution with a constant gauge field, which is pure AdS. Both solutions preserve half of the supersymmetries at a special value of the Wilson line. There is a phase transition between these two saddle-points as a function of the Wilson line precisely at the supersymmetric point. Thus, the supersymmetric solutions are degenerate, at least at the supergravity level. We extend this discussion to one of the Romans solutions in four dimensions when the Euclidean boundary is S1× Σg where Σg is a Riemann surface with genus g > 0. We speculate that the supersymmetric state of the CFT on the boundary is dual to a superposition of the two degenerate geometries.

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