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3 results

  • 33 - Nontrivial topologies: gravitational instantons, Taub–NUT, KK monopole, and Gödel spacetimes

  • Horatiu Nastase, Universidade Estadual Paulista, São Paulo
  • Book:
    General Relativity
    Published online:
    24 April 2025
    Print publication:
    08 May 2025, pp 362-374

  • Summary

    We describe nontrivial topologies. First, we describe the Taub–NUT solutions. Then the Taub–NUT of Hawking and the Taub solution, as gravitational instantons. Then the Eguchi–Hanson metric, obtained from a Yang–Mills like instanton ansatz. Then the Gibbons–Hawking multi-instanton. The KK monopole is shown to be an example of application of the Taub–NUT instanton. Finally, we describe the Gödel Universe, a rotating solution with closed timelike curves (CTCs), even though the source is standard, just dust matter and cosmological constant.

  • 23 - General relativity solutions and the gauge theory double copy

  • Horatiu Nastase, Universidade Estadual Paulista, São Paulo
  • Book:
    General Relativity
    Published online:
    24 April 2025
    Print publication:
    08 May 2025, pp 248-260

  • Summary

    We find out how to write general relativity solutions as double copies of gauge theory solutions. As a motivation, we first consider the KLT relations and the BCJ relations, for graviton quantum amplitudes as double copies of gluon quantum amplitudes. Then we consider the double copy for solutions in Kerr–Schild coordinates. As examples, we consider the Schwarzschild black hole, the Kerr black hole, pp waves, and the Taub–NUT solution. We define the Weyl double copy and write it for the general Petrov type D solution.

  • 46 - Vielbein-Spin Connection Formulation of General Relativity and Gravitational Instantons

  • from Part III - Other Spins or Statistics; General Relativity
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 441-454

  • Summary

    We start by defining the vielbein-spin connection formulation of general relativity and the Palatini formalism. Next we define the Taub–NUT solutions and their analytical continuation, the Euclidean gravitational instanton defined by Hawking. Next, following the example of the Yang–Mills instanton, we write the Einstein equations in Euclidean signature as self-duality equations for the spin connection, which we solve by an instanton ansatz, obtaining the Eguchi–Hanson metric, and example of ALE space. We rewrite it and generalize it in the form of the Gibbons–Hawking multi-instanton solution.