Light bending in a two black hole metric

Abstract

We discuss the propagation of light in the C-metric. We discover that null geodesics admit circular orbits only for a certain family of orbital cones. Explicit analytic formulae are derived for the orbital radius and the corresponding opening angle fixing the cone. Furthermore, we prove that these orbits based on a saddle point in the effective potential are Jacobi unstable. This completes the stability analysis done in previous literature and allows us to probe into the light bending in a two black hole metric. More precisely, by constructing a suitable tetrad in the Newmann-Penrose formalism, we show that light propagation in this geometry is shear-free, irrotational, and a light beam passing by a C-black hole undergoes a focussing process. An exact analytic formula for the compression factor $\theta$ is derived and discussed. Furthermore, we study the weak and strong gravitational lensing when both the observer and the light ray belong to the aforementioned family of invariant cones. In particular, we obtain formulae allowing to calculate the deflection angle in the weak and strong gravitational lensing regimes.

27 pages, 3 figures, updated bibliography

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• Conservation of distortion of gravitationally lensed images
• Lightlike Geodesics and Gravitational Lensing in the Spacetime of an Accelerating Black Hole
• Geodesics motion of test particles around Schwarzschild-Klinkhamer wormhole with topological defects and gravitational lensing
• Null geodesics in the C-metric with cosmological constant
• Laser propagation in Rindler accelerated reference frame based on matrix optics
• Relevant scales for the $C$-metric with positive cosmological constant
• Magnetised relativistic accretion disc around a spinning, electrically charged, accelerating black hole: case of C-metric
• The Tomimatsu-Sato metric reloaded
• C-metric in a (nut)shell
• Casimir energy of hyperbolic orbifolds with conical singularities
• Gravitational Lensing by Charged Accelerating Black Holes