scholarly journals Extended General Relativity for a Curved Universe

2020 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Positive Curvature ◽  
Boundary Term ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Conformal Curvature ◽  
Curvature Term ◽  
Extended Field ◽  
Matter Energy

The recent Planck Legacy release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background, which endorses the early universe positive curvature with a confidence level exceeding 99%. Although general relativity performs accurately in the present universe where spacetime is almost flat, the necessity of dark matter/energy and the lost boundary term might be signs of its incompleteness. Utilising Einstein–Hilbert action, I present extended field equations considering the pre-existing universal curvatures. The new extended field equations are inclusive of Einstein field equations in addition to the boundary term and the conformal curvature term contributions.

scholarly journals Extended General Relativity for a Curved Universe

2020 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Positive Curvature ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Conformal Curvature ◽  
Present Universe ◽  
Extended Field ◽  
Hilbert Action ◽  
Matter Energy

The Planck Legacy recent release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background, which endorses the early universe positive curvature with a confidence level greater than 99%. Although General Relativity performs accurately in the present universe where spacetime is almost flat, its lost boundary term and the need of dark matter/energy might indicate its incompleteness. By utilising the Einstein–Hilbert action, this letter presents new extended field equations considering pre-existing universal curvatures and boundary contributions. The extended field equations are inclusive of Einstein field equations in addition to the boundary and the conformal curvature terms, which could remove the singularities from the theory.

scholarly journals Extended General Relativity for a Curved Universe

2021 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Early Universe ◽  
Cold Dark Matter ◽  
Positive Curvature ◽  
Boundary Term ◽  
Radius Of Curvature ◽  
Field Equations ◽  
Extended Field ◽  
Background Curvature

The recent Planck Legacy release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB). Notably, this amplitude is higher than that estimated by the lambda cold dark matter model (ΛCDM), which endorses the positive curvature of the early Universe with a confidence level greater than 99%. Although General Relativity (GR) performs accurately in the local/present Universe where spacetime is almost flat, its lost boundary term, incompatibility with quantum mechanics and the necessity of dark matter and dark energy might indicate its incompleteness. By utilising the Einstein–Hilbert action, this study presents extended field equations considering the pre-existing/background curvature and the boundary contribution. The extended field equations consist of Einstein field equations with a conformal transformation feature in addition to the boundary term, which could remove singularities from the theory and facilitate its quantisation. The extended equations have been utilised to derive the evolution of the Universe with reference to the scale factor of the early Universe and its radius of curvature.

scholarly journals Extended General Relativity for a Curved Universe

2020 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Gravitational Lensing ◽  
Cold Dark Matter ◽  
Positive Curvature ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Cold Dark Matter Model ◽  
Order Of Magnitude ◽  
Dark Matter Model

The Planck Legacy recent release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background, which confirms the early universe positive curvature with a confidence level exceeding 99%. Besides, the observed gravitational lensing within several galaxy clusters is higher than that estimated through the standard lambda cold dark matter model by an order of magnitude. While general relativity works perfectly well in the present universe where the spacetime is almost flat, it should be enhanced to account for the pre-existing universal curvature. This study presents new enhanced field equations utilising Einstein–Hilbert action. The enhanced field equations are reduced to Einstein field equations in a flat universe.

scholarly journals Extended General Relativity for a Conformally Curved Universe

2021 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Cold Dark Matter ◽  
Power Spectra ◽  
Boundary Term ◽  
Field Equations ◽  
Microwave Background ◽  
Extended Field ◽  
Background Curvature ◽  
Invariance Theory

The recent Planck Legacy release confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra. Notably, this amplitude is higher than that estimated by the lambda cold dark matter model (ΛCDM), which endorses a positively curved early Universe with a confidence level greater than 99%. Although General Relativity (GR) performs accurately in the local/present Universe where spacetime is almost flat, its lost boundary term, incompatibility with Quantum Mechanics and the necessity of dark matter/energy could indicate its incompleteness. By utilising the Einstein–Hilbert action, this letter presents extended field equations by considering the pre-existing/background curvature and the boundary contribution. The extended field equations consist of Einstein field equations with a conformal transformation feature in addition to the boundary term, which can remove singularities, satisfy a conformal invariance theory and facilitate its quantisation.

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.

scholarly journals Extended Field Equations for Conformally Curved Spacetime

2021 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
Early Universe ◽  
Positive Curvature ◽  
Power Spectra ◽  
Brane World ◽  
Field Equations ◽  
Microwave Background ◽  
Spacetime Curvature ◽  
Extended Field ◽  
Invariance Theory ◽  
Positively Curved

The recent Planck Legacy release has confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which prefers a positively curved early Universe with a confidence level greater than 99%. In addition, the spacetime curvature of the entire galaxy differs from one galaxy to another due to their diverse energy densities. This study considers both the implied positive curvature of the early Universe and the curvature across the entire galaxy as the curvature of ‘the background or the 4D bulk’ and distinguishes it from the localized curvature that is induced in the bulk by the presence of comparably smaller celestial objects that are regarded as ‘relativistic 4D branes’. Branes in different galaxies experience different bulk curvatures, thus their background or bulk curvature should be taken into consideration along with their energy densities when finding their induced curvatures. To account for the interaction between the bulk and branes, this paper presents extended field equations in terms of brane-world modified gravity consisting of conformal Einstein field equations with a boundary term, which could remove the singularities and satisfy a conformal invariance theory. A visualization of the evolution of the 4D relativistic branes over the conformal space-time of the 4D bulk is presented.

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.

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