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Covariant Wick rotation: action, entropy, and holonomies.

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Title: Covariant Wick rotation: action, entropy, and holonomies.
Authors: Singh, Raghvendra1 (AUTHOR) raghvendra@imsc.res.in, Kothawala, Dawood2 (AUTHOR)
Source: European Physical Journal C -- Particles & Fields. Mar2023, Vol. 83 Issue 3, p1-12. 12p.
Subjects: Entropy, Holonomy groups, Vector fields, Rotational motion, Quantum gravity, Action theory (Psychology), Curvature
Abstract: Given an arbitrary Lorentzian metric g ab and a nowhere vanishing, timelike vector field u a , one can construct a class of metrics g ^ ab which have Euclidean signature in a specific domain, with a transition to Lorentzian regime occurring on some hypersurface Σ orthogonal to u a . Geometry associated with g ^ ab has been shown to yield some remarkable insights for classical and quantum gravity. In this work, we focus on studying the implications of this geometry for thermal effects in curved spacetimes and compare and contrast the results with those obtained through conventional Euclidean methods. We show that the expression for entropy computed using g ^ ab for simple field theories and Lanczos–Lovelock actions differ from Wald entropy by additional terms depending on extrinsic curvature. We also compute the holonomy associated with loops lying partially or wholly in the Euclidean regime in terms of extrinsic curvature and acceleration and compare it with the well-known expression for temperature. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Covariant Wick rotation: action, entropy, and holonomies.
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  Data: <searchLink fieldCode="AR" term="%22Singh%2C+Raghvendra%22">Singh, Raghvendra</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> raghvendra@imsc.res.in</i><br /><searchLink fieldCode="AR" term="%22Kothawala%2C+Dawood%22">Kothawala, Dawood</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. Mar2023, Vol. 83 Issue 3, p1-12. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Entropy%22">Entropy</searchLink><br /><searchLink fieldCode="DE" term="%22Holonomy+groups%22">Holonomy groups</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+fields%22">Vector fields</searchLink><br /><searchLink fieldCode="DE" term="%22Rotational+motion%22">Rotational motion</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+gravity%22">Quantum gravity</searchLink><br /><searchLink fieldCode="DE" term="%22Action+theory+%28Psychology%29%22">Action theory (Psychology)</searchLink><br /><searchLink fieldCode="DE" term="%22Curvature%22">Curvature</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Given an arbitrary Lorentzian metric g ab and a nowhere vanishing, timelike vector field u a , one can construct a class of metrics g ^ ab which have Euclidean signature in a specific domain, with a transition to Lorentzian regime occurring on some hypersurface Σ orthogonal to u a . Geometry associated with g ^ ab has been shown to yield some remarkable insights for classical and quantum gravity. In this work, we focus on studying the implications of this geometry for thermal effects in curved spacetimes and compare and contrast the results with those obtained through conventional Euclidean methods. We show that the expression for entropy computed using g ^ ab for simple field theories and Lanczos–Lovelock actions differ from Wald entropy by additional terms depending on extrinsic curvature. We also compute the holonomy associated with loops lying partially or wholly in the Euclidean regime in terms of extrinsic curvature and acceleration and compare it with the well-known expression for temperature. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1140/epjc/s10052-023-11340-1
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      – Code: eng
        Text: English
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        PageCount: 12
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    Subjects:
      – SubjectFull: Entropy
        Type: general
      – SubjectFull: Holonomy groups
        Type: general
      – SubjectFull: Vector fields
        Type: general
      – SubjectFull: Rotational motion
        Type: general
      – SubjectFull: Quantum gravity
        Type: general
      – SubjectFull: Action theory (Psychology)
        Type: general
      – SubjectFull: Curvature
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      – TitleFull: Covariant Wick rotation: action, entropy, and holonomies.
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            NameFull: Singh, Raghvendra
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              M: 03
              Text: Mar2023
              Type: published
              Y: 2023
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