Special Issue "Broken Symmetry in Curved Spacetime and Gravity"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 August 2018)

Special Issue Editor

Guest Editor
Dr. Charles D. Lane

Department of Physics Astronomy and Geology, Berry College, GA, USA
Website | E-Mail
Interests: fundamental symmetries; high-energy physics; mathematical physics

Special Issue Information

Modern physics rests on a foundation of two fundamental theories: General Relativity (GR) and the Standard Model (SM). Each theory agrees extremely well with experiments in a certain domain. However, the predictions of the theories disagree with each other in certain situations. Therefore, GR and the SM are likely to be low-energy approximations to some more fundamental theory. A major current goal in physics is to determine the nature of this more fundamental theory.

The most natural approach to learning about the fundamental theory is to look for situations where GR and the SM strongly disagree; in such situations, at least one of these theories must make predictions that are clearly wrong. Unfortunately, all known situations where the theories strongly disagree are untenable to study experimentally. This leads us to consider an alternate approach—suppose that one or both of these theories is slightly wrong in a situation where we can perform experiments with extremely high precision. Careful study of these high-precision experiments could reveal a violation of one of the current theories. This is the approach taken in studies of spacetime symmetry violation.

Keywords

  • Spacetime symmetry
  • Local Lorentz Symmetry
  • Local Lorentz Violation
  • Tests of General Relativity
  • CPT
  • Standard-Model Extension
  • Finsler Geometry

Published Papers (6 papers)

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Research

Open AccessArticle
Constraints on Lorentz Invariance Violation from Optical Polarimetry of Astrophysical Objects
Symmetry 2018, 10(11), 596; https://doi.org/10.3390/sym10110596
Received: 7 September 2018 / Revised: 31 October 2018 / Accepted: 2 November 2018 / Published: 5 November 2018
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Abstract
Theories of quantum gravity suggest that Lorentz invariance, the fundamental symmetry of the Theory of Relativity, may be broken at the Planck energy scale. While any deviation from conventional Physics must be minuscule in particular at attainable energies, this hypothesis motivates ever more [...] Read more.
Theories of quantum gravity suggest that Lorentz invariance, the fundamental symmetry of the Theory of Relativity, may be broken at the Planck energy scale. While any deviation from conventional Physics must be minuscule in particular at attainable energies, this hypothesis motivates ever more sensitive tests of Lorentz symmetry. In the photon sector, astrophysical observations, in particular polarization measurements, are a very powerful tool because tiny deviations from Lorentz invariance will accumulate as photons propagate over cosmological distances. The Standard-Model Extension (SME) provides a theoretical framework in the form of an effective field theory that describes low-energy effects due to a more fundamental quantum gravity theory by adding additional terms to the Standard Model Lagrangian. These terms can be ordered by the mass dimension d of the corresponding operator and lead to a wavelength, polarization, and direction dependent phase velocity of light. Lorentz invariance violation leads to an energy-dependent change of the Stokes vector as photons propagate, which manifests itself as a rotation of the polarization angle in measurements of linear polarization. In this paper, we analyze optical polarization measurements from 63 Active Galactic Nuclei (AGN) and Gamma-ray Bursts (GRBs) to search for Lorentz violating signals. We use both spectropolarimetric measurements, which directly constrain the change of linear polarization angle, as well as broadband spectrally integrated measurements. In the latter, Lorentz invariance violation manifests itself by reducing the observed net polarization fraction. Any observation of non-vanishing linear polarization thus leads to constraints on the magnitude of Lorentz violating effects. We derive the first set limits on each of the 10 individual birefringent coefficients of the minimal SME with d = 4 , with 95% confidence limits on the order of 10−34 on the dimensionless coefficients. Full article
(This article belongs to the Special Issue Broken Symmetry in Curved Spacetime and Gravity)
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Open AccessArticle
Lorentz-Violating Gravity Models and the Linearized Limit
Symmetry 2018, 10(10), 490; https://doi.org/10.3390/sym10100490
Received: 7 September 2018 / Revised: 9 October 2018 / Accepted: 10 October 2018 / Published: 12 October 2018
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Abstract
Many models in which Lorentz symmetry is spontaneously broken in a curved spacetime do so via a “Lorentz-violating” (LV) vector or tensor field, which dynamically takes on a vacuum expectation value and provides additional local geometric structure beyond the metric. The kinetic terms [...] Read more.
Many models in which Lorentz symmetry is spontaneously broken in a curved spacetime do so via a “Lorentz-violating” (LV) vector or tensor field, which dynamically takes on a vacuum expectation value and provides additional local geometric structure beyond the metric. The kinetic terms of such a field will not necessarily be decoupled from the kinetic terms of the metric, and will generically lead to a set of coupled equations for the perturbations of the metric and the LV field. In some models, however, the imposition of certain additional conditions can decouple these equations, yielding an “effective equation” for the metric perturbations alone. The resulting effective equation may depend on the metric in a gauge-invariant way, or it may be gauge-dependent. The only two known models yielding gauge-invariant effective equations involve differential forms; I show in this work that the obvious generalizations of these models do not yield gauge-invariant effective equations. Meanwhile, I show that a gauge-dependent effective equation may be obtained from any “tensor Klein–Gordon” model under similar assumptions. Finally, I discuss the implications of this work in the search for Lorentz-violating gravitational effects. Full article
(This article belongs to the Special Issue Broken Symmetry in Curved Spacetime and Gravity)
Open AccessArticle
Relating Noncommutative SO(2,3) Gravity to the Lorentz-Violating Standard-Model Extension
Symmetry 2018, 10(10), 480; https://doi.org/10.3390/sym10100480
Received: 3 September 2018 / Revised: 1 October 2018 / Accepted: 3 October 2018 / Published: 11 October 2018
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Abstract
We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension (SME). We analyze in detail [...] Read more.
We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension (SME). We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) model and the Standard-Model Extension. As part of the analysis, we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background. Full article
(This article belongs to the Special Issue Broken Symmetry in Curved Spacetime and Gravity)
Open AccessFeature PaperArticle
Is There Any Symmetry Left in Gravity Theories with Explicit Lorentz Violation?
Symmetry 2018, 10(10), 433; https://doi.org/10.3390/sym10100433
Received: 15 August 2018 / Revised: 14 September 2018 / Accepted: 18 September 2018 / Published: 25 September 2018
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Abstract
It is well known that a theory with explicit Lorentz violation is not invariant under diffeomorphisms. On the other hand, for geometrical theories of gravity, there are alternative transformations, which can be best defined within the first-order formalism and that can be regarded [...] Read more.
It is well known that a theory with explicit Lorentz violation is not invariant under diffeomorphisms. On the other hand, for geometrical theories of gravity, there are alternative transformations, which can be best defined within the first-order formalism and that can be regarded as a set of improved diffeomorphisms. These symmetries are known as local translations, and among other features, they are Lorentz covariant off shell. It is thus interesting to study if theories with explicit Lorentz violation are invariant under local translations. In this work, an example of such a theory, known as the minimal gravity sector of the Standard Model Extension, is analyzed. Using a robust algorithm, it is shown that local translations are not a symmetry of the theory. It remains to be seen if local translations are spontaneously broken under spontaneous Lorentz violation, which are regarded as a more natural alternative when spacetime is dynamic. Full article
(This article belongs to the Special Issue Broken Symmetry in Curved Spacetime and Gravity)
Open AccessFeature PaperArticle
(Gravitational) Vacuum Cherenkov Radiation
Symmetry 2018, 10(10), 424; https://doi.org/10.3390/sym10100424
Received: 1 September 2018 / Revised: 15 September 2018 / Accepted: 15 September 2018 / Published: 21 September 2018
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Abstract
This work reviews our current understanding of Cherenkov-type processes in vacuum that may occur due to a possible violation of Lorentz invariance. The description of Lorentz violation is based on the Standard Model Extension (SME). To get an overview as general as possible, [...] Read more.
This work reviews our current understanding of Cherenkov-type processes in vacuum that may occur due to a possible violation of Lorentz invariance. The description of Lorentz violation is based on the Standard Model Extension (SME). To get an overview as general as possible, the most important findings for vacuum Cherenkov radiation in Minkowski spacetime are discussed. After doing so, special emphasis is put on gravitational Cherenkov radiation. For a better understanding, the essential properties of the gravitational SME are recalled in this context. The common grounds and differences of vacuum Cherenkov radiation in Minkowski spacetime and in the gravity sector are emphasized. Full article
(This article belongs to the Special Issue Broken Symmetry in Curved Spacetime and Gravity)
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Open AccessArticle
The (A)symmetry between the Exterior and Interior of a Schwarzschild Black Hole
Symmetry 2018, 10(9), 366; https://doi.org/10.3390/sym10090366
Received: 30 July 2018 / Revised: 15 August 2018 / Accepted: 22 August 2018 / Published: 27 August 2018
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Abstract
A black hole in a Schwarzschild spacetime is considered. A transformation is proposed that describes the relationship between the coordinate systems exterior and interior to an event horizon. The application of this transformation permits considerations of the (a)symmetry of a range of phenomena [...] Read more.
A black hole in a Schwarzschild spacetime is considered. A transformation is proposed that describes the relationship between the coordinate systems exterior and interior to an event horizon. The application of this transformation permits considerations of the (a)symmetry of a range of phenomena taking place on both sides of the event horizon. The paper investigates two distinct problems of a uniformly accelerated particle. In one of these, although the equations of motion are the same in the regions on both sides, the solutions turn out to be very different. This manifests the differences of the properties of these two ranges. Full article
(This article belongs to the Special Issue Broken Symmetry in Curved Spacetime and Gravity)
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