Optical drift effects in general relativity

Abstract

We consider the question of determining the optical drift effects in general relativity, i.e. the rate of change of the apparent position, redshift, Jacobi matrix, angular distance and luminosity distance of a distant object as registered by an observer in an arbitrary spacetime. We present a fully relativistic and covariant approach, in which the problem is reduced to a hierarchy of ODE's solved along the line of sight. The 4-velocities and 4-accelerations of the observer and the emitter and the geometry of the spacetime along the line of sight constitute the input data. We build on the standard relativistic geometric optics formalism and extend it to include the time derivatives of the observables. In the process we obtain two general, non-perturbative relations: the first one between the gravitational lensing, represented by the Jacobi matrix, and the apparent position drift, also called the cosmic parallax, and the second one between the apparent position drift and the redshift drift. The applications of the results include the theoretical study of the drift effects of cosmological origin (so-called real-time cosmology) in numerical or exact Universe models.

Matches the version published in JCAP

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• Multipole decomposition of redshift drift -- model independent mapping of the expansion history of the Universe
• Redshift drift cosmography for model-independent cosmological inference
• Reduced phase space optics for general relativity: Symplectic ray bundle transfer
• Redshift drift in a universe with structure I: Lemaitre-Tolman-Bondi structures with arbitrary angle of entry of light
• Geometric optics in relativistic cosmology: new formulation and a new observable
• Weighing the spacetime along the line of sight using times of arrival of electromagnetic signals
• Observed Angles and Geodesic Light-Cone Coordinates
• The Instantaneous Redshift Difference of Gravitationally Lensed Images: Theory and Observational Prospects
• Direct geometrical measurement of the Hubble constant from galaxy parallax: predictions for the Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope
• Redshift drift in a universe with structure II: Light rays propagated through a Newtonian N-body simulation
• Strong Gravitational Lensing in Horndeski theory
• Relative efficiency of three mechanisms of vector fields growth in a random media
• BiGONLight: light propagation with bi-local operators in Numerical Relativity
• The effect of our local motion on the Sandage-Loeb test of the cosmic expansion
• Non-perturbative results for the luminosity and area distances
• Redshift drift in a universe with structure III: Numerical relativity
• 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