Geometric optics in general relativity using bilocal operators

Abstract

We consider the standard problem of observational astronomy, i.e. the observations of light emission from a distant region of spacetime in general relativity. The goal is to describe the changes between the measurements of the light performed by a sample of observers slightly displaced with respect to each other and moving with different 4-velocities and 4-accelerations. In our approach, all results of observations can be expressed as functions of the kinematic variables, describing the motions of the observers and the emitting bodies with respect to their local inertial frames, and four linear bilocal geodesic operators, describing the influence of the spacetime geometry on light propagation. The operators are functionals of the curvature tensor along the line of sight. The results are based on the assumption that the regions of emissions and observations are sufficiently small so that the spacetime curvature effects are negligible within each of them, although they are significant for the light propagation between them. The new formulation provides a uniform approach to optical phenomena in curved spacetimes and, as an application, we discuss the problem of a fully relativistic definition of the parallax and position drifts (or proper motions). We then use the results to construct combinations of observables which are completely insensitive to the motion of both the observer and the emitter. These combinations by construction probe the spacetime geometry between the observation and emission regions and in our formalism we may express them as functionals of the Riemann tensor along the line of sight. For short distances one of these combinations depends only on the matter content along the line of sight. This opens up the possibility to measure the matter content of a spacetime in a tomography-like manner irrespective of the motions of the emitter and the observer.

arXiv commentMinor revision

References in corpus (44)

• GAIA: Composition, Formation and Evolution of the Galaxy
• Gaia Data Release 2: using Gaia parallaxes
• The motion of point particles in curved spacetime
• Gravitational Lensing
• Gravitational Lensing in Astronomy
• The astrometric core solution for the Gaia mission. Overview of models, algorithms and software implementation
• General relativity and cosmic structure formation
• gevolution: a cosmological N-body code based on General Relativity
• Effects of nonlinear inhomogeneity on the cosmic expansion with numerical relativity
• Real-time Cosmology
• Departures from the FLRW Cosmological Model in an Inhomogeneous Universe: A Numerical Examination
• Parallax Beyond a Kiloparsec from Spatially Scanning the Wide Field Camera 3 on the Hubble Space Telescope
• Effect of Peculiar Motion in Weak Lensing
• Black Hole Universe: Time Evolution
• Persistent gravitational wave observables: general framework
• Evolution of a periodic eight-black-hole lattice in numerical relativity
• Inhomogeneous Cosmology with Numerical Relativity
• Integration of inhomogeneous cosmological spacetimes in the BSSN formalism
• Fermi Coordinates and Penrose Limits
• Cosmic Parallax: possibility of detecting anisotropic expansion of the universe by very accurate astrometry measurements
• Evolution of a family of expanding cubic black-hole lattices in numerical relativity
• Black Hole Universe with $\Lambda$
• A new approach to the propagation of light-like signals in perturbed cosmological backgrounds
• Redshift propagation equations in the ${\beta }^{\prime }\ne 0$ Szekeres models
• The trouble with Hubble: Local versus global expansion rates in inhomogeneous cosmological simulations with numerical relativity
• Swiss-cheese models and the Dyer-Roeder approximation
• Gravitational lensing beyond geometric optics: I. Formalism and observables
• Geodesic deviation at higher orders via covariant bitensors
• A covariant treatment of cosmic parallax
• Optical drift effects in general relativity
• Direction and redshift drifts for general observers and their applications in cosmology
• Cosmic Parallax as a probe of late time anisotropic expansion
• 3+1 geodesic equation and images in numerical spacetimes
• Light propagation through black-hole lattices
• Generalized deviation equation and determination of the curvature in General Relativity
• Can Cosmic Parallax Distinguish Between Anisotropic Cosmologies?
• Reduced phase space optics for general relativity: Symplectic ray bundle transfer
• Calculating Observables in Inhomogeneous Cosmologies I: General Framework
• Roulettes: A weak lensing formalism for strong lensing - II. Derivation and analysis
• Roulettes: A weak lensing formalism for strong lensing - I. Overview
• Repeatable light paths in the shearfree normal cosmological models
• Exact inhomogeneous models and the drift of light rays induced by nonsymmetric flow of the cosmic medium
• Repeatable light paths in the conformally flat cosmological models
• Local spacetime effects on gyroscope systems

Cited by in corpus (23)

• Persistent gravitational wave observables: general framework
• Solving the curvature and Hubble parameter inconsistencies through structure formation-induced curvature
• Persistent gravitational wave observables: Nonlinear plane wave spacetimes
• Revisiting timelike and null geodesics in the Schwarzschild spacetime: general expressions in terms of Weierstrass elliptic functions
• Reduced phase space optics for general relativity: Symplectic ray bundle transfer
• On the covariance of scalar averaging and backreaction in relativistic inhomogeneous cosmology
• Cosmological distances with general-relativistic ray tracing: framework and comparison to cosmographic predictions
• Geometric optics in relativistic cosmology: new formulation and a new observable
• Tetrad formalism for exact cosmological observables
• Persistent gravitational wave observables: Nonlinearities in (non-)geodesic deviation
• Weighing the spacetime along the line of sight using times of arrival of electromagnetic signals
• Direct detection of the cosmic expansion: the redshift drift and the flux drift
• The Instantaneous Redshift Difference of Gravitationally Lensed Images: Theory and Observational Prospects
• Isolating non-linearities of light propagation in inhomogeneous cosmologies
• BiGONLight: light propagation with bi-local operators in Numerical Relativity
• Gravitational wave memory and its effects on particles and fields
• Bilocal geodesic operators in static spherically-symmetric spacetimes
• Algebraic symmetries of the observables on the sky: Variable emitters and observers
• Testing the null energy condition with precise distance measurements
• 1+1+2 covariant formulation of light propagation in spacetime
• The averaging problem on the past null cone in inhomogeneous dust cosmologies
• Axion-Photon Conversion Signals from Neutron Stars with Spacetime Curvature Accounted for in the Magnetosphere Model
• Gaussian beams and caustic avoidance in gravitational optics