Hidden symmetries from distortions of the conformal structure

Abstract

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.

arXiv comment37 pages, 1 figure, Latex2e source file, minor changes to match published version

References in corpus (54)

• The Relation between Physical and Gravitational Geometry
• Measurement of the Kerr Spin Parameter by Observation of a Compact Object's Shadow
• Very Special Relativity
• Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
• General Very Special Relativity is Finsler Geometry
• Black holes, hidden symmetries, and complete integrability
• The General Very Special Relativity in Finsler Cosmology
• Curvature radius and Kerr black hole shadow
• Disformal Transformations, Veiled General Relativity and Mimetic Gravity
• Polynomial SUSY in Quantum Mechanics and Second Derivative Darboux Transformation
• Vanishing Scalar Invariant Spacetimes in Higher Dimensions
• The Memory Effect for Plane Gravitational Waves
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Soft Gravitons & the Memory Effect for Plane Gravitational Waves
• Lie and Noether symmetries of geodesic equations and collineations
• Lie - point and variational symmetries in minisuperspace Einstein's gravity
• Nonlinear Supersymmetry, Quantum Anomaly and Quasi-Exactly Solvable Systems
• Quasinormal Modes of Black Holes with Multiple Photon Spheres
• Matrix Hamiltonians: SUSY approach to hidden symmetries
• Conformal symmetry classes for pp-wave spacetimes
• On the nature of fermion-monopole supersymmetry
• Dynamical symmetries in Brans-Dicke cosmology
• Quantum integrability of quadratic Killing tensors
• Memory, Penrose Limits and the Geometry of Gravitational Shockwaves and Gyratons
• Chaos in pp-wave spacetimes
• Scaling and conformal symmetries for plane gravitational waves
• Chaos in a modified Henon-Heiles system describing geodesics in gravitational waves
• Extended disformal approach in the scenario of Rainbow Gravity
• Geodesic motion in Bogoslovsky-Finsler Spacetimes
• Nonlinear superconformal symmetry of a fermion in the field of a Dirac monopole
• Disformal Transformations in Scalar-Torsion Gravity
• Memory effects in Kundt wave spacetimes
• On the disformal invariance of the Dirac equation
• Second Order Symmetries of the Conformal Laplacian
• Conformal symmetries and integrals of the motion in pp waves with external electromagnetic fields
• Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background
• Quadratic first integrals of autonomous conservative dynamical systems
• The regularity of geodesics in impulsive pp-waves
• "Kepler Harmonies" and conformal symmetries
• Hidden symmetry and (super)conformal mechanics in a monopole background
• On Integrability of the Geodesic Deviation Equation
• The Work-Energy Relation for Particles on Geodesics in the pp-Wave Spacetimes
• The geometry of null-like disformal transformations
• Integrability of geodesic motions in curved manifolds through non-local conserved charges
• Lukash plane waves, revisited
• Projective collineations of decomposable spacetimes generated by the Lie point symmetries of geodesic equations
• Nonlinear supersymmetry as a hidden symmetry
• Higher order first integrals of autonomous dynamical systems
• Hidden Symmetries in Deformed Very Special Relativity
• Lie Symmetries of Non-Relativistic and Relativistic Motions
• Disformal transformations and the motion of a particle in semi-classical gravity
• Conformal bridge in a cosmic string background
• On the hypotheses of Penrose's singularity theorem under disformal transformations
• Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator

Cited by in corpus (5)

• Observational constraints on two cosmological models of $f(Q)$ theory
• Schrödinger Symmetry in Gravitational Mini-Superspaces
• Various disguises of the Pais-Uhlenbeck oscillator
• Quadratic first integrals of constrained autonomous conservative dynamical systems with fixed energy
• Eisenhart-Duval lift, Nonlocal Conservation laws and Painlevé Analysis in Scalar field Cosmology