Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric optics in general relativity using bilocal operators   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.

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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: nlin
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th