Algebraic symmetries of the observables on the sky: Variable emitters and observers
arXiv:2405.05105 · doi:10.1103/PhysRevD.110.064043
Abstract
In this paper we prove a number of exact relations between optical observables, such as trigonometric parallax, position drift and the proper motion of a luminous source in addition to the variations of redshift and the viewing angle. These relations are valid in general relativity for any spacetime and they are of potential interest for astrometry and precise cosmology. They generalize the well-known Etherington's reciprocity relation between the angular diameter distance and the luminosity distance. Similar to Etherington's relation, they hold independently of the spacetime metric, the positions and the motions of a light source or an observer. We show that those relations follow from the symplectic property of the bi-local geodesic operator, i.e., the geometric object that describes the light propagation between two distant regions of a spacetime. The set of relations we present is complete in the sense that no other relations between those observables should hold in general. In the meantime, we develop the mathematical machinery of the bi-local approach to light propagation in general relativity and its corresponding Hamiltonian formalism.
v2: Published version. 28 pages, 4 figures, 2 tables
References in corpus (16)
- Strong-field Gravity Tests with the Double Pulsar
- Time drift of cosmological redshifts as a test of the Copernican principle
- Time Dilation in Type Ia Supernova Spectra at High Redshift
- Redshift Drift in LTB Void Universes
- Cosmic Parallax: possibility of detecting anisotropic expansion of the universe by very accurate astrometry measurements
- Another look at redshift drift and the backreaction conjecture
- Light propagation in a homogeneous and anisotropic universe
- Geodesic deviation at higher orders via covariant bitensors
- Cosmic Parallax in Ellipsoidal Universe
- Cosmic Parallax as a probe of late time anisotropic expansion
- Redshift drift in axially symmetric quasi-spherical Szekeres models
- Stochastic gravitational wave background constraints from Gaia DR3 astrometry
- Redshift drift in a pressure-gradient cosmology
- Redshift drift cosmography with ELT and SKAO measurements
- Redshift drift in a universe with structure I: Lemaitre-Tolman-Bondi structures with arbitrary angle of entry of light
- Towards Cosmography of the Local Universe