Physics

Gravitation

Gravitational field

Deflection (physics)

Mathematics

Mathematical physics

Gravitational lens

Galaxy

General relativity

Gauss–Bonnet theorem

Einstein

Weak gravitational lensing

Photon

Gaussian curvature

Geodesic

Curvature

Geometry

Quantum mechanics

Redshift

Strong gravitational lensing

Geodesics in general relativity

Classical mechanics

Physical review. D/Physical review. D.

In this work we extend the approach used in [Emanuel Gallo and Osvaldo M. Moreschi, Phys. Rev. D 83, 083007 (2011)] to the study of weak gravitational lensing in a plasma medium. First, we present expressions for the deflection angle and optical scalars in terms of the components of the energy-momentum tensor for spherically symmetric lenses surrounded by a cold nonmagnetized plasma. Second, we show that the same expressions can be deduced using the Gauss-Bonnet theorem. Finally, we establish a correspondence between the spatial orbits of photons in a nonhomogeneous plasma and the nongeodesic curves followed by test massive particles whose dynamics also depend on an external central field. As an application, we use the Gauss-Bonnet theorem to compute the deflection angle of the non-geodesic trajectories followed by relativistic test massive charged particles in a Reissner-Nordstr\"om spacetime.

Gravitational lensing in dispersive media and deflection angle of charged massive particles in terms of curvature scalars and energy-momentum tensor