Entropy, Cosmic Inflation and the Theory of Relativity: In Honour of Prof. Øyvind Grøn

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Cosmology".

Deadline for manuscript submissions: closed (15 January 2023) | Viewed by 5242

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Department of Mathematics and Natural Sciences, University of Stavanger, 4036 Stavanger, Norway
Interests: riemannian geometry/lorentzian geometry; lie groups/algebras; homogeneous spaces; relativity; cosmology (mathematical aspects); alternative theories of gravity; classification issues for exact solutions in GR

Special Issue Information

Dear Colleagues,

It is our pleasure to invite you to contribute to a Universe topical collection titled "Entropy, Cosmic Inflation and the Theory of Relativity: In Honour of Prof. Øyvind Grøn".

The aim is to gather a collection of contributions that relate to the scientific works of Øyvind Grøn. His doctoral thesis was titled “Repulsive gravitation”.

Early works of Grøn were concerned with the asynchronous formulation of relativistic kinematics and dynamics. Then, he wrote several articles on the relativistically rotating disk and proceeded with several works concerned with inertial dragging.

Together with professor Erik Eriksen, he subsequently worked out a series of papers on electromagnetic radiation and the principle of equivalence.

At the same time, Øyvind Grøn and Harald Soleng produced several articles together about different topics, for example the Einstein–Cartan theory.

Then, in a series of papers with Steinar Johannesen, conformally flat spacetimes were studied, and they showed that the Levi-Civita-Bertotti-Robinson solution of Einstein’s field equations represents spacetime outside a charged spherical domain wall.

Grøn also studied Kaluza-Klein theory, and together with Matthew T. Aadne, the Nash gravitational theory. Furthermore, together with Johannesen, Bræck and Ivar Farup, he studied rotating universe models.

Observational consequences of different inflationary models were recently reviewed by Grøn. He has earlier written about viscous inflationary universe models together with professor Iver Brevik.

Grøn also showed how an anisotropic universe isotropizes due to the presence of Lorentz invariant vacuum energy, for which he introduced the acronym LIVE. 

Another topic studied by Grøn and co-workers—Sigbjørn Hervik, Håvard Alnes, Morad Amarzguioui and Øystein Elgarøy—was gravitational entropy.

Together with Simen Bræck, Grøn introduced the concept “river of space”, and with Bræck and Ivar Farup, the concept “causal cosmic mass”. Grøn has also written several papers on the twin paradox—one together with Simen Bræck.

Prof. Dr. Sigbjørn Hervik
Guest Editor

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Keywords

  • the asynchronous formulation of relativity
  • the ehrenfest paradox and physics in rotating reference frames
  • the twin paradox
  • electrodynamics of radiating charges
  • effects of repulsive gravitation such as isotropization of anisotropic universe models
  • conformally flat spacetimes
  • rotating universe models
  • gravitation and entropy
  • the inflationary era
  • inertial dragging
  • Kaluza-Klein theory

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Published Papers (3 papers)

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Research

13 pages, 301 KiB  
Article
Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes
by Simen Braeck
Universe 2023, 9(3), 120; https://doi.org/10.3390/universe9030120 - 26 Feb 2023
Cited by 1 | Viewed by 1308
Abstract
In axistationary, asymptotically flat spacetimes, zero angular momentum observers (ZAMOs) define an absolute standard of non-rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue that on a global scale the only physically meaningful [...] Read more.
In axistationary, asymptotically flat spacetimes, zero angular momentum observers (ZAMOs) define an absolute standard of non-rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue that on a global scale the only physically meaningful concept is that of relative rotation. The argument is substantiated by solving Einstein’s equations for an approximate thin shell model, where we maintain a degree of freedom, by relaxing the natural assumption of vanishing rotation at asymptotic infinity, at the outset of the analysis. The solution reveals that Einstein’s equations only determine differences in the rotation rate of ZAMOs, thereby establishing the concept of relative rotation globally. The interpretation of rotation as relative in a global context is inherently linked to the freedom to transform between coordinate systems rotating relative to each other, implying that an arbitrary ZAMO located at any radius may claim to be the one that is non-rotating on a global scale, and that the notion of an asymptotic Lorentz frame relative to which one may measure absolute rotation is devoid of any meaning. The concept of rotation in Kerr spacetime is then briefly discussed in the context of this interpretation. Full article
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13 pages, 281 KiB  
Article
On the General Entangled State and Quantum Decoherence
by Abasalt Rostami and Javad T. Firouzjaee
Universe 2022, 8(10), 508; https://doi.org/10.3390/universe8100508 - 26 Sep 2022
Cited by 6 | Viewed by 1267
Abstract
We study the primary entanglement effect on the decoherence of reduced-density matrices of scalar fields, which interact with other fields or independent mode functions. We study the (leading) tree-level evolution of the scalar bispectrum due to a coupling between two scalar fields. We [...] Read more.
We study the primary entanglement effect on the decoherence of reduced-density matrices of scalar fields, which interact with other fields or independent mode functions. We study the (leading) tree-level evolution of the scalar bispectrum due to a coupling between two scalar fields. We show that the primary entanglement has a significant role in the decoherence of the given quantum state. We find that the existence of such an entanglement could couple dynamical equations coming from a Schrödinger equation. We show that if one wants to see no effect of the entanglement parameter in the decohering of the quantum system, then the ground state eigenvalues of the interaction terms in the Hamiltonian cannot be independent of each other Generally, including the primary entanglement destroys the independence of the interaction terms in the ground state. We show that the imaginary part of the entanglement parameter plays an important role in the decoherence process without posing any specific restriction to the interaction terms. Our results could be generalized to every scalar quantum field theory with a well-defined quantization of its fluctuations in a given curved space-time. Full article
25 pages, 595 KiB  
Article
Consequences of the Improved Limits on the Tensor-to-Scalar Ratio from BICEP/Planck, and of Future CMB-S4 Measurements, for Inflationary Models
by Øyvind G. Grøn
Universe 2022, 8(9), 440; https://doi.org/10.3390/universe8090440 - 24 Aug 2022
Cited by 2 | Viewed by 1315
Abstract
More than 30 inflationary models are confronted with the recently improved limit on the tensor-to-scalar ratio presented by the Planck team. I show that a few more models are falsified due to this sharper restriction. Additionally, I discuss possible consequences of CMB-S4 observations [...] Read more.
More than 30 inflationary models are confronted with the recently improved limit on the tensor-to-scalar ratio presented by the Planck team. I show that a few more models are falsified due to this sharper restriction. Additionally, I discuss possible consequences of CMB-S4 observations for these inflationary models. The results are summarized in a table. Full article
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