Abstract
Beyond the Einstein–Maxwell model, electromagnetic field might couple with gravitational field through the Weyl tensor. In order to provide one of the missing puzzles of the whole physical picture, we investigate weak deflection lensing for photons coupled to the Weyl tensor in a Schwarzschild black hole under a unified framework that is valid for its two possible polarizations. We obtain its coordinate-independent expressions for all observables of the geometric optics lensing up to the second order in the terms of varepsilon which is the ratio of the angular gravitational radius to angular Einstein radius of the lens. These observables include bending angle, image position, magnification, centroid and time delay. The contributions of such a coupling on some astrophysical scenarios are also studied. We find that, in the cases of weak deflection lensing on a star orbiting the Galactic Center Sgr A*, Galactic microlensing on a star in the bulge and astrometric microlensing by a nearby object, these effects are beyond the current limits of technology. However, measuring the variation of the total flux of two weak deflection lensing images caused by the Sgr A* might be a promising way for testing such a coupling in the future.
Highlights
Gravitational lensing has become an invaluable tool in astronomy, cosmology and gravitational physics [1,2,3,4]
In a summary, based on the current limit of the technology and the specific circumstance of the Sgr A*, the impact of the photons coupling to the Weyl tensor in the Schwarzschild black hole is unable to be detected in the observables of weak deflection lensing, while measuring on the variation of the total flux of two images might be a promising way for testing such a coupling in the future
In order to provide one of the missing puzzles of the whole physical picture of photons coupled to Weyl tensor in a Schwarzschild black hole, we investigate its weak deflection lensing, as an extension of the previous works on its
Summary
Gravitational lensing has become an invaluable tool in astronomy, cosmology and gravitational physics [1,2,3,4]. We will study weak deflection lensing for photons coupled to Weyl tensor in a Schwarzschild black hole, which was absent in the literature. By focusing on coordinate-invariant quantities, we obtain all of its geometric optics lensing observables, which include bending angle, image position, magnification, centroid and time delay. These observables are worked out to the second order in the perturbation parameter ε which is the ratio of the angular gravitational radius to angular Einstein radius of the lens. 2, after the unified effective metric for photons coupled to the Weyl tensor in a Schwarzschild black hole with two polarization directions is briefly reviewed, we will derive its light bending angle that is expressed with invariant quantities.
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