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

Carla Cederbaum, Karim Mosani

TL;DR

This work addresses the trapped photon region in the domain of outer communication for sub-extremal Kerr-Newman and Kerr-Sen spacetimes. It adopts a direct Cederbaum–Jahns style approach, using first-integrals $E$, $L$, and the Killing-tensor constant $\mathcal{K}$ to construct maps on the tangent and cotangent bundles and to identify the trapped set via a pair of submersion arguments. The main result is that the image $\tilde{P}\subset T\mathcal{N}$ of the trapped photon region is a five-dimensional submanifold with topology $SO(3)\times\mathbb{R}^2$, with a detailed topological classification reducing to $SO(3)$ on a six-dimensional slice; the analysis extends Teo/O'Neill style arguments to the Kerr–Newman and Kerr–Sen geometries and includes a nonexistence result for zero-energy trapped photons. These findings have potential implications for black hole shadows, gravitational lensing, and stability analyses in charged, rotating spacetimes.

Abstract

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.

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

TL;DR

This work addresses the trapped photon region in the domain of outer communication for sub-extremal Kerr-Newman and Kerr-Sen spacetimes. It adopts a direct Cederbaum–Jahns style approach, using first-integrals , , and the Killing-tensor constant to construct maps on the tangent and cotangent bundles and to identify the trapped set via a pair of submersion arguments. The main result is that the image of the trapped photon region is a five-dimensional submanifold with topology , with a detailed topological classification reducing to on a six-dimensional slice; the analysis extends Teo/O'Neill style arguments to the Kerr–Newman and Kerr–Sen geometries and includes a nonexistence result for zero-energy trapped photons. These findings have potential implications for black hole shadows, gravitational lensing, and stability analyses in charged, rotating spacetimes.

Abstract

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 in each setup. The proof adapts the method of Cederbaum and Jahns for sub-extremal Kerr spacetime.
Paper Structure (5 sections, 2 theorems, 10 equations)

This paper contains 5 sections, 2 theorems, 10 equations.

Table of Contents

  1. Introduction
  2. The setup and trapped null geodesics
  3. Geometry
  4. Topology
  5. Technical Distinctions from the Sub-Extremal Kerr Case

Key Result

Theorem 1

In both sub-extremal Kerr--Newman and Kerr--Sen spacetimes (collectively denoted by $(\mathcal{N},h)$) that contain trapped photons, the image $\Tilde{P} \subset T\mathcal{N}$ of the trapped photon region $P$ (located in the domain of outer communication), under the canonical map defined in expressi

Theorems & Definitions (2)

  • Theorem 1
  • Proposition 1