Note on complex metrics, complex time, and periodic universes

Briscese, Fabio

doi:10.1103/physrevd.105.126028

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“…See also the early work [4] and, for an alternative admissibility proposal, [5]. Since its inception, Witten's proposal has been investigated further in various contexts (see [6][7][8][9][10][11][12] for a partial list of references related to the present work).…”

Section: Introductionmentioning

confidence: 99%

A note on the admissibility of complex BTZ metrics

Basile

Campoleoni

Raeymaekers

2023

J. High Energ. Phys.

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We perform a nontrivial check of Witten’s recently proposed admissibility criterion for complex metrics. We consider the ‘quasi-Euclidean’ metrics obtained from continuing the BTZ class of metrics to imaginary time. Of special interest are the overspinning metrics, which are smooth in this three-dimensional context. Their inclusion as saddle points in the gravitational path integral would lead to puzzling results in conflict with those obtained using other methods. It is therefore encouraging that the admissibility criterion discards them. For completeness, we perform an analysis of smoothness and admissibility for the family of quasi-Euclidean BTZ metrics at all values of the mass and angular momentum.

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