Caustics of $1/r^n$ binary gravitational lenses: from galactic haloes to exotic matter

Abstract

We investigate the caustic topologies for binary gravitational lenses made up of two objects whose gravitational potential declines as $1/r^n$. With $n<1$ this corresponds to power-law dust distributions like the singular isothermal sphere. The $n>1$ regime can be obtained with some violations of the energy conditions, one famous example being the Ellis wormhole. Gravitational lensing provides a natural arena to distinguish and identify such exotic objects in our Universe. We find that there are still three topologies for caustics as in the standard Schwarzschild binary lens, with the main novelty coming from the secondary caustics of the close topology, which become huge at higher $n$. After drawing caustics by numerical methods, we derive a large amount of analytical formulae in all limits that are useful to provide deeper insight in the mathematics of the problem. Our study is useful to better understand the phenomenology of galaxy lensing in clusters as well as the distinct signatures of exotic matter in complex systems.

28 pages, 19 figures, focus expanded to galactic haloes

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Cited by in corpus (13)

• Strong deflection limit analysis and gravitational lensing of an Ellis wormhole
• Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime
• Strong gravitational lensing --- A probe for extra dimensions and Kalb-Ramond field
• Gravitational lensing in the Simpson-Visser black-bounce spacetime in a strong deflection limit
• Light curves of light rays passing through a wormhole
• Retrolensing by a wormhole at deflection angles $\pi$ and $3\pi$
• Extended source effect on microlensing light curves by an Ellis wormhole
• Gravitational lensing by using the 0th order of affine perturbation series of the deflection angle of a ray near a photon sphere
• Gravitational lensing by exotic objects
• High energy particle collisions in static, spherically symmetric black-hole-like wormholes
• Dual-Component Plasma Lens Models
• Microlensing effect of charged spherically symmetric wormhole
• Gravitational lensing by two photon spheres in a black-bounce spacetime in strong deflection limits