Trapped photon region in the phase space of sub-extremal Kerr-Newman and Kerr-Sen spacetimes

We analyse the geometry and topology of the trapped photon region in the domain of outer communication of sub-extremal Kerr-Newman and Kerr-Sen spacetimes. Specifically, we show that its projection to the (co-)tangent bundle forms a five-dimensional submanifold with topology $SO(3)\times {\mathbb{R}}^2$ in each setup. The proof adapts the method of Cederbaum and Jahns for sub-extremal Kerr spacetime.