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Geodesics on metrics of self-dual Taub-Nut type

Chuxiao Liu, Qingtao Pu

Abstract

Geodesic equations are solved when at least two of $τ$, $θ$, $\varphi$ are constant on metrics of self-dual Taub-NUT type. They can also be solved also on self-dual Taub-NUT metrics if only $r$, $θ$ or $\varphi$ is constant. However, the explicit solution of the geodesic equations is not available yet if only $τ$ is constant.

Geodesics on metrics of self-dual Taub-Nut type

Abstract

Geodesic equations are solved when at least two of , , are constant on metrics of self-dual Taub-NUT type. They can also be solved also on self-dual Taub-NUT metrics if only , or is constant. However, the explicit solution of the geodesic equations is not available yet if only is constant.

Paper Structure

This paper contains 10 sections, 6 theorems, 71 equations.

Table of Contents

  1. Introduction
  2. Metrics of self-dual Taub-NUT type and geodesic equations
  3. Geodesics on metrics of self-dual Taub-NUT type
  4. Geodesics for constant $\tau$,$\theta$,$\varphi$
  5. Geodesics for constant $\theta$,$\varphi$
  6. Geodesics for constant $\theta\in (0,\pi)$, $\tau$
  7. Geodesics for constant $\varphi$,$\tau$
  8. Geodesics for constant $r$
  9. Geodesics for constant $\varphi$
  10. Geodesics for constant $\theta$

Key Result

Theorem 3.1

The geodesics for metrics of self-dual Taub-NUT type with constant $\theta$,$\varphi$,$\tau$ and passing through $r=n$ with conditions satisfy

Theorems & Definitions (6)

  • Theorem 3.1
  • Theorem 3.2
  • Theorem 3.3
  • Theorem 3.4
  • Lemma 3.1
  • Theorem 3.5