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<p>In a previous work, the regular cosmological volume function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\tau _V\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mi>V</mi> </msub> </math></EquationSource> </InlineEquation> was introduced as an alternative to the regular cosmological time function of Andersson, Galloway, and Howard. Building on work by Chruściel, Grant and Minguzzi, in this paper we show that in many cases of interest, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\tau _V\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mi>V</mi> </msub> </math></EquationSource> </InlineEquation> is a continuously differentiable temporal function. This leads to a canonical splitting of the metric tensor, and induces a canonical “Wick-rotated” Riemannian metric. We also provide some further results and examples related to the cosmological time and volume functions.</p>

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Differentiability and other properties of the cosmological volume function

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月26日

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  • Leonardo García-Heveling

摘要

In a previous work, the regular cosmological volume function \(\tau _V\) τ V was introduced as an alternative to the regular cosmological time function of Andersson, Galloway, and Howard. Building on work by Chruściel, Grant and Minguzzi, in this paper we show that in many cases of interest, \(\tau _V\) τ V is a continuously differentiable temporal function. This leads to a canonical splitting of the metric tensor, and induces a canonical “Wick-rotated” Riemannian metric. We also provide some further results and examples related to the cosmological time and volume functions.