Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator

Elbistan, Mahmut

doi:10.1016/j.nuclphysb.2022.115846

Cited by 7 publications

(1 citation statement)

References 82 publications

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“…Among the various studies regarding geodesic equations, a great number is devoted to the motion in a pp-wave background [27][28][29][30][31][32][33][34][35][36]. The symmetries of the pp-wave metrics have been extensively studied in several works [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Hidden symmetries from distortions of the conformal structure

Dimakis

2022

Preprint

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It is well established that the mass parameter breaks the conformal symmetries in the case of geodesic motion. The proper conformal Killing vectors cease to generate conserved charges when non-null geodesics are considered. We examine how the introduction of the mass is actually related to the appearance of appropriate distortions in the conformal sector, which lead to new conservation laws. As a prominent example we use a general pp-wave metric, which exploits this property to the maximum. We study the necessary geometric conditions, so that such types of distortions are applicable. We show that the relative vectors are generators of disformal transformations and prove their connection to higher order (hidden) symmetries. Except from the pp-wave geometry, we also provide an additional example in the form of the de Sitter metric. Again, the proper conformal Killing vectors can be appropriately distorted to generate conserved quantities for massive geodesics. Subsequently, we proceed by introducing an additional symmetry breaking effect. The latter is realized by considering a Bogoslovsky type of line-element, which involves a Lorentz violating parameter. We utilize once more the pp-wave case as a guide to study how the broken symmetries -this time also related to Killing vectors -are substituted by distortions of the original generators. We further analyze and discuss the necessary geometric conditions that lead to the emergence of these distortions.

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Section: Introductionmentioning

confidence: 99%

Hidden symmetries from distortions of the conformal structure

Dimakis

2022

Preprint

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Conformally related vacuum gravitational waves and their symmetries

Zhao,

Zhang,

Horváthy

2024

J. High Energ. Phys.

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A special conformal transformation which carries a vacuum gravitational wave into another vacuum one is built by using Möbius-redefined time. It can either transform a globally defined vacuum wave into a vacuum sandwich wave, or carry the gravitational wave into itself. The first type, illustrated by linearly and circularly polarised vacuum plane gravitational waves, permutes the symmetries and the geodesics. Our second type is a pp wave with conformal O(1, 2) symmetry. An example inspired by molecular physics which seems to have escaped attention so far is an anisotropic generalisation of the familiar inverse-square profile and is reminiscent of Aichelburg-Sexl ultraboosts. The particle can escape, or perform circular periodic motion, or fall into the singularity.

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