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Smoothness of the future and past trapped sets in Kerr-Newman-Taub-NUT spacetimes

Claudio F. Paganini, Marius A. Oancea

Abstract

We consider the sets of future/past trapped null geodesics in the exterior region of a sub-extremal Kerr-Newman-Taub-NUT spacetime. We show that, from the point of view of any timelike observer outside of such a black hole, trapping can be understood as two smooth sets of spacelike directions on the celestial sphere of the observer.

Smoothness of the future and past trapped sets in Kerr-Newman-Taub-NUT spacetimes

Abstract

We consider the sets of future/past trapped null geodesics in the exterior region of a sub-extremal Kerr-Newman-Taub-NUT spacetime. We show that, from the point of view of any timelike observer outside of such a black hole, trapping can be understood as two smooth sets of spacelike directions on the celestial sphere of the observer.

Paper Structure

This paper contains 7 sections, 3 theorems, 31 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Kerr-Newman-Taub-NUT Spacetime
  3. Geodesic Equations
  4. Trapping as a Set of Directions
  5. Framework
  6. The trapped sets
  7. Conclusion

Key Result

Lemma 8

The sets $\mathbb{T}_+(p)$ and $\mathbb{T}_-(p)$ are circles on the celestial sphere of any timelike observer at any regular point of symmetry in the exterior region of any subextremal Kerr-Newman-Taub-NUT spacetime.

Figures (1)

  • Figure 1: Conformal diagrams giving a schematic representation of elements of the sets in Definition \ref{['def:futinf']}.

Theorems & Definitions (15)

  • Remark 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Lemma 8
  • proof
  • Theorem 9
  • ...and 5 more