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.

💡 Research Summary

The paper investigates the geometry and topology of the trapped photon region (TPR) in the domain of outer communication (DOC) of sub‑extremal Kerr‑Newman and Kerr‑Sen spacetimes. By treating both families of solutions within a unified metric ansatz—characterized by two radial functions (K(r)) and (f(r)) that specialize to the Kerr‑Newman ((K=r^{2},,f=Mr-e^{2}/2)) and Kerr‑Sen ((K=r^{2}(1+e^{2}/(Mr)),,f=Mr)) cases—the authors are able to apply a single analytical framework.

A trapped photon is defined as a null geodesic whose Boyer‑Lindquist radial coordinate remains constant. The motion of any geodesic in these axisymmetric, stationary spacetimes is completely integrable: there exist four first integrals—energy (E), axial angular momentum (L), the Carter‑type constant (K), and the null condition (q=0). Proposition 1 establishes that, under the mild conditions (f(0)\le0), bijectivity of (K(r)) on (