Critique of the use of geodesics in astrophysics and cosmology

Abstract

Since particles obey wave equations, in general one is not free to postulate that particles move on the geodesics associated with test particles. Rather, for this to be the case one has to be able to derive such behavior starting from the equations of motion that the particles obey, and to do so one can employ the eikonal approximation. To see what kind of trajectories might occur we explore the domain of support of the propagators associated with the wave equations. For a minimally coupled massless scalar field the domain of support in curved space is shown to not be restricted to the light cone, while for a conformally coupled massless scalar field the curved space domain is only restricted to the light cone if it propagates in a conformal to flat background. Consequently, eikonalization does not in general lead to null geodesics for curved space massless rays even though it does lead to straight line trajectories in flat spacetime. Equal remarks apply to the massless conformal invariant Maxwell equations. However, for massive particles one does obtain standard geodesic behavior this way, since they do not propagate on the light cone to begin with. Thus depending on how big the curvature actually is, in principle, even if not necessarily in practice, the standard null-geodesic-based gravitational bending formula and the general behavior of propagating light rays are in need of modification in regions with high enough curvature. We show that relativistic eikonalization has an intrinsic light-front structure, and show that eikonalization in a theory with local conformal symmetry leads to trajectories that are only globally conformally symmetric. Normals to wavefronts follow the eikonal trajectories, with these trajectories being the trajectories along which energy and momentum are transported.

51 pages. In flat space normals to wavefronts are geodesic. We show that the curved space generalization is to curved space wavefront normals, and in curved space these normals do not have to be geodesic. This is the final version, which is to appear in Classical and Quantum Gravity

References in corpus (17)

• The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited
• Impact of a global quadratic potential on galactic rotation curves
• Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies
• Solution to the ghost problem in fourth order derivative theories
• Precise analytic treatment of Kerr and Kerr-(anti) de Sitter black holes as gravitational lenses
• Fake Conformal Symmetry in Conformal Cosmological Models
• The Relevance of the Cosmological Constant for Lensing
• Exact gravitational lensing in conformal gravity and Schwarzschild-de Sitter spacetime
• Conformal gravity does not predict flat galaxy rotation curves
• Gauge Natural Formulation of Conformal Theory of Gravity
• The cosmological background and the "external field" in Modified Gravity (MOG)
• Exact solution to perturbative conformal cosmology in the recombination era
• External Field Effect in Gravity
• Cosmological Fluctuations on the Light Cone
• Exact solution to perturbative conformal cosmology from recombination until the current era
• Scalar and vector tail radiation from the interior of the lightcone
• Structure of conformal gravity in the presence of a scale breaking scalar field

Cited by in corpus (3)

• Electromagnetic signatures of strong-field gravity from accreting black holes
• The effect of dark matter discreteness on light propagation
• Structure of conformal gravity in the presence of a scale breaking scalar field