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<p>The gravitational path integral on <i>S</i><sup>2</sup> × <i>S</i><sup>2</sup> can be interpreted either as evaluating a contribution to the norm of the Hartle-Hawking wavefunction conditional on spatial <i>S</i><sup>1</sup> × <i>S</i><sup>2</sup> topology, or the pair creation rate of black holes in de Sitter. Both interpretations are distinguished at the quantum level. The former requires the path integral to be real and the latter to be imaginary. We develop a formalism to efficiently compute the phase of the gravitational path integral on Einstein spaces. We apply it to a broad class of spacetimes and in particular <i>S</i><sup>2</sup> × <i>S</i><sup><i>D−</i>2</sup>, finding it to be real and positive. We generalize some of the analysis to cases with charge and rotation.</p>

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The phase of the gravitational path integral

  • 期刊论文

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  • 发表日期：

    2025年7月3日

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  • Xiaoyi Shi,
  • Gustavo J. Turiaci

摘要

The gravitational path integral on S2 × S2 can be interpreted either as evaluating a contribution to the norm of the Hartle-Hawking wavefunction conditional on spatial S1 × S2 topology, or the pair creation rate of black holes in de Sitter. Both interpretations are distinguished at the quantum level. The former requires the path integral to be real and the latter to be imaginary. We develop a formalism to efficiently compute the phase of the gravitational path integral on Einstein spaces. We apply it to a broad class of spacetimes and in particular S2 × SD−2, finding it to be real and positive. We generalize some of the analysis to cases with charge and rotation.