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 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 Generalized Phenomenological Models of Dark Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Prasenjit Paul ◽  
Rikpratik Sengupta
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Density ◽  
Cosmological Constant ◽  
Phenomenological Models ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Free Parameters ◽  
The Universe ◽  
Matter Energy

It was first observed at the end of the last century that the universe is presently accelerating. Ever since, there have been several attempts to explain this observation theoretically. There are two possible approaches. The more conventional one is to modify the matter part of the Einstein field equations, and the second one is to modify the geometry part. We shall consider two phenomenological models based on the former, more conventional approach within the context of general relativity. The phenomenological models in this paper consider a Λ term firstly a function of a¨/a and secondly a function of ρ, where a and ρ are the scale factor and matter energy density, respectively. Constraining the free parameters of the models with the latest observational data gives satisfactory values of parameters as considered by us initially. Without any field theoretic interpretation, we explain the recent observations with a dynamical cosmological constant.

FIVE-DIMENSIONAL DUST COLLAPSE WITH COSMOLOGICAL CONSTANT

2007 ◽  
Vol 16 (01) ◽  
pp. 53-64 ◽  
Author(s):  
S. G. GHOSH ◽  
D. W. DESHKAR ◽  
N. N. SASTE
Keyword(s):  
Cosmological Constant ◽  
Causal Structure ◽  
Cosmic Censorship ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Positive Cosmological Constant ◽  
Naked Singularities ◽  
Spherical Collapse ◽  
Strong Curvature

We study the five-dimensional spherical collapse of an inhomogeneous dust in the presence of a positive cosmological constant. The general interior solutions, in the closed form, of the Einstein field equations, i.e. the 5D Tolman–Bondi–de Sitter, is obtained which in turn is matched to the exterior 5D Schwarzschild–de Sitter. It turns out that the collapse proceeds in the same way as in the Minkowski background, i.e. the strong curvature naked singularities form and thus violate the cosmic censorship conjecture. A brief discussion on the causal structure singularities and horizons is also given.

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.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

scholarly journals "Gravitationally Lensed Gravitation" (GLG)

2021 ◽  
Author(s):  
Andreas Boenke
Keyword(s):  
General Relativity ◽  
Field Strength ◽  
Free Fall ◽  
Gravitational Effect ◽  
Gravitational Lens ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Optical Illusions ◽  
Spacetime Curvature ◽  
Background Object

The intention of this paper is to point out a remarkable hitherto unknown effect of General Relativity. Starting from fundamental physical principles and phenomena arising from General Relativity, it is demonstrated by a simple Gedankenexperiment that a gravitational lens enhances not only the light intensity of a background object but also its gravitational field strength by the same factor. Thus, multiple images generated by a gravitational lens are not just optical illusions, they also have a gravitational effect at the location of the observer! The "Gravitationally Lensed Gravitation" (GLG) may help to better understand the rotation curves of galaxies since it leads to an enhancement of the gravitational interactions of the stars. Furthermore, it is revealed that besides a redshift of the light of far distant objects, the cosmic expansion also causes a corresponding weakening of their gravitational effects. The explanations are presented entirely without metric representation and tensor formalism. Instead, the behavior of light is used to indicate the effect of spacetime curvature. The gravitation is described by the field strength which is identical to the free fall acceleration. The new results thus obtained provide a reference for future numerical calculations based on the Einstein field equations.

The Einstein field equations

2019 ◽  
pp. 52-58
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Newtonian Gravity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Noether’S Theorem ◽  
Geodesic Deviation ◽  
Fundamental Equations ◽  
Hilbert Action ◽  
Qualitative Discussion

The Einstein field equations are the fundamental equations of general relativity. After a brief qualitative discussion of geodesic deviation and Newtonian gravity, this chapter derives the field equations from the Einstein-Hilbert action. The chapter contains a derivation of Noether’s theorem and the consequent conservation laws, and a brief discussion of generalizations of the Einstein-Hilbert action.

Wormhole in 5D Kaluza–Klein cosmology

2017 ◽  
Vol 32 (07) ◽  
pp. 1750023 ◽  
Author(s):  
Gargi Biswas ◽  
B. Modak
Keyword(s):  
Boundary Conditions ◽  
Cosmological Constant ◽  
Dimensional Reduction ◽  
Dimensional Space ◽  
Field Equations ◽  
Positive Cosmological Constant ◽  
Euclidean Field ◽  
Pure Gravity ◽  
Imaginary Field ◽  
Kaluza Klein

We present wormhole as a solution of Euclidean field equations as well as the solution of the Wheeler–deWitt (WD) equation satisfying Hawking–Page wormhole boundary conditions in (4 + 1)-dimensional Kaluza–Klein cosmology. The wormholes are considered in the cases of pure gravity, minimally coupled scalar (imaginary) field and with a positive cosmological constant assuming dynamical extra-dimensional space. In above cases, wormholes are allowed both from Euclidean field equations and WD equation. The dimensional reduction is possible.

Gravitational waves in general relativity IX. Conserved quantities

1966 ◽  
Vol 294 (1436) ◽  
pp. 112-122 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Source Distribution ◽  
Conserved Quantities ◽  
Direct Solution ◽  
Multipole Moments ◽  
Einstein Field Equations ◽  
Field Equations

This paper shows how the ten conserved quantities, recently discovered by E. T. Newman and R. Penrose by essentially geometrical techniques, arise in a direct solution of the Einstein field equations. For static fields it is shown that five of the conserved quantities vanish while the remaining five are expressed in terms of the multipole moments of the source distribution.

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