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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Phi _{01}=\Phi _{12}=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mn>01</mn> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">Φ</mi> <mn>12</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. We prove that these conditions determine the solutions up to a freedom in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Phi _{11}\pm 3\Lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mn>11</mn> </msub> <mo>±</mo> <mn>3</mn> <mi mathvariant="normal">Λ</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Non-vacuum Metrics for the Newman-Unti-Tamburino Background: A Coordinate-Free Approach to Diverging and Twisting Solutions

  • 期刊论文

  • 发表日期：

    2026年5月22日

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

摘要

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 \(\Phi _{01}=\Phi _{12}=0\) Φ 01 = Φ 12 = 0 . We prove that these conditions determine the solutions up to a freedom in \(\Phi _{11}\pm 3\Lambda \) Φ 11 ± 3 Λ .