论文标题
协方差灯芯旋转的几何方面
Geometric aspects of covariant Wick rotation
论文作者
论文摘要
我们讨论了指标的通用几何属性$ \ wideHat {g} _ {ab} $由lorentzian Metric $ g_ {ab} $构建的，以及无处消失的，超出的正交正交，时间级别的矢量vector Field $ u^a $。公制$ {\ wideHat g} _ {ab} $在某个域中具有欧几里得签名，其过渡到洛伦兹签名的过渡发生在某些超曲面$σ$ qunthoconal到$ u^a $。与$ {\ wideHat g} _ {ab} $相关的几何形状最近已被证明可以为经典和量子重力提供出色的新见解。在这项工作中，我们证明了几个一般结果适用于与非零加速度$ a^i $的一致性相关的空间。我们以最大对称性为例的示例是动态球形对称空间和空间的示例。我们还在弯曲的空间中与地平线的弯曲空间中的热效应有关这种形式主义。具体来说，我们讨论：（i）循环的全能部分位于欧几里得政权中。我们表明，欧几里得域对固体的贡献完全由$σ$的外部曲率$ k_ {ab} $和加速度$ a^i $确定。 （ii）我们还使用这种形式主义来计算简单场理论的熵，并为兰开斯 - 洛沃克重力，Bekenstein-Hawking Entropy关系获得叶片依赖性校正。
We discuss the generic geometric properties of metrics $\widehat {g}_{ab}$ constructed from Lorentzian metric $g_{ab}$ and a nowhere vanishing, hypersurface orthogonal, timelike vector field $u^a$. The metric ${\widehat g}_{ab}$ has Euclidean signature in a certain domain, with the transition to Lorentzian signature occurring at some hypersurface $Σ$ orthogonal to $u^a$. Geometry associated with ${\widehat g}_{ab}$ has recently been shown to yield remarkable new insights for classical and quantum gravity. In this work, we prove several general results applicable in physically relevant spacetimes for congruences $u^i$ with non-zero acceleration $a^i$. We present as examples the cases of dynamical spherically symmetric spacetimes and spacetimes with maximal symmetry. We also investigate this formalism within the context of thermal effects in curved spacetimes with horizons. Specifically, we discuss: (i) the Holonomy of loops lying partially or wholly in the Euclidean regime. We show that the contribution of the Euclidean domain to holonomy is completely determined by extrinsic curvature $K_{ab}$ of $Σ$ and acceleration $a^i$. (ii) We also compute entropy using this formalism for simple field theories and obtain foliation dependent corrections for the Lanczos-Lovelock gravity, Bekenstein-Hawking entropy relation in four spacetime dimensions.
