Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime

Gravitational lensing by the light sphere of compact objects like black holes and wormholes will give us information on the compact objects. In this paper, we provide an improved strong deflection limit analysis in a general asymptotically flat, static, spherically symmetric spacetime. The strong deflection limit analysis also works in ultrastatic spacetimes. As an example of an ultrastatic spacetime, we reexamine the deflection angle in the strong deflection limit in an Ellis wormhole spacetime. Using the strong deflection limit, we obtain the deflection angle analytically for the Reissner-Nordström spacetime. The point of the improvement is the definition of a standard variable in the strong deflection limit analysis. We show that the choice of the variable is as important as the choice of the coordinates and we conclude that one should choose a proper variable for a given spacetime.

Figure 1

$b_c/M$, $\overline{a}$, and $\overline{b}$ in the Reissner-Nordström black hole spacetime. The solid (red), dot-dashed (green), and dashed (blue) curves denote $b_c/M$, $\overline{a}$, and $\overline{b}$, respectively.