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Non-vacuum metrics for the Newman-Unti-Tamburino background: A coordinate-free approach to diverging and twisting solutions

Ayşe Hümeyra Bilge, Tolga Birkandan, Tekin Dereli, Gulay Karakaya

Abstract

The geometry of the Newman-Unti-Tamburino (NUT) vacuum solution is characterized as the unique Petrov Type D vacuum metric such that the two double principal null directions form an integrable distribution. We study expanding and twisting non-vacuum Type D metrics in this geometry, with the additional assumption $Φ_{01}=Φ_{12}=0$. We prove that these conditions determine the solutions up to a freedom in $Φ_{11}\pm 3Λ$.

Non-vacuum metrics for the Newman-Unti-Tamburino background: A coordinate-free approach to diverging and twisting solutions

Abstract

The geometry of the Newman-Unti-Tamburino (NUT) vacuum solution is characterized as the unique Petrov Type D vacuum metric such that the two double principal null directions form an integrable distribution. We study expanding and twisting non-vacuum Type D metrics in this geometry, with the additional assumption . We prove that these conditions determine the solutions up to a freedom in .
Paper Structure (10 sections, 58 equations)

This paper contains 10 sections, 58 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Assumptions and gauge transformations
  4. Newman-Penrose equations
  5. Algebraic relations in the NP system
  6. Integrability of the NP system
  7. Admissible Sources
  8. Examples
  9. CONCLUSIONS
  10. Example Metrics Consistent with Our Results