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A coordinate-free approach to obtaining exact solutions in general relativity: The Newman-Unti-Tamburino solution revisited

Emir Baysazan, Ayse Humeyra Bilge, Tolga Birkandan, Tekin Dereli

Abstract

The Newman-Unti-Tamburino (NUT) solution is characterized as the unique Petrov Type $D$ vacuum metric such that the two double principal null directions form an integrable distribution. The uniqueness of the NUT is established by evaluating the integrability conditions of the Newman-Penrose equations up to $SL(2,\mathbb{C})$ transformations, resulting in a coordinate-free characterization of the solution.

A coordinate-free approach to obtaining exact solutions in general relativity: The Newman-Unti-Tamburino solution revisited

Abstract

The Newman-Unti-Tamburino (NUT) solution is characterized as the unique Petrov Type vacuum metric such that the two double principal null directions form an integrable distribution. The uniqueness of the NUT is established by evaluating the integrability conditions of the Newman-Penrose equations up to transformations, resulting in a coordinate-free characterization of the solution.

Paper Structure

This paper contains 11 sections, 106 equations.

Table of Contents

  1. Introduction
  2. Overdetermined systems of partial differential equations
  3. Canonical forms of Type $D$ metrics
  4. $SL(2,\mathbb{C})$ transformations
  5. Type $D$ VACUUM METRICS
  6. Characterization of the NUT Solution
  7. The Symmetry Algebra
  8. Non-twisting metrics
  9. Commutation relations for the metric components
  10. The Newman-Unti-Tamburino (NUT) solution in local coordinates
  11. NP Equations for Type $D$ Metrics