Gravitational lensing in Brill spacetimes

Abstract

We consider the Brill metric which is an electrovacuum solution to Einstein's field equation. It depends on three parameters, a mass parameter $m$, a NUT parameter $l$ and a charge parameter $e$. If the charge parameter is small, the metric describes a black hole; if it is sufficiently big, it describes a wormhole. We determine the relevant lensing features both in the black-hole and in the wormhole case. In particular, we give formulas for the photon spheres, for the angular radius of the shadow and for the deflection angle. We illustrate the lensing features with the help of an effective potential and in terms of embedding diagrams. To that end we make use of the fact that each lightlike geodesic is contained in a (coordinate) cone and that it is a geodesic of a Riemannian optical metric on this cone. By the Gauss-Bonnet theorem, the sign of the Gaussian curvature of the optical metric determines the sign of the deflection angle. In the wormhole case the deflection angle may be negative which means that light rays are repelled from the center.

References in corpus (6)

• Calculating black hole shadows: Review of analytical studies
• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times
• Geometric Approach to Circular Photon Orbits and Black Hole Shadows
• Curvatures, Photon Spheres and Black Hole Shadows
• A Morse-theoretical analysis of lensing in wormhole spacetimes

Cited by in corpus (6)

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• Gravitational Lensing of Schwarzschild and Charged Black Holes Immersed in Perfect Fluid Dark Matter Halo
• Traversable Wormholes in Minimally Geometrical Deformed Trace-Free Gravity using Gravitational Decoupling
• Gravitational Lensing of Massive Particles in the Charged NUT Spacetime
• Modified Kerr black holes surrounded by dark matter spike
• The scalar angular Teukolsky equation and its solution for the Taub-NUT spacetime