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<p>We extend the notion of surface gravity to a wide class of non-smooth null hypersurfaces in a spacetime of arbitrary dimension. The lower differentiability presents a number of new challenges, since nearly all the the standard techniques applicable to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^k\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mi>k</mi> </msup> </math></EquationSource> </InlineEquation> null hypersurfaces with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> fail in that context. Nevertheless, we are able to obtain suitable geometric conditions under which a continuous null section with constant surface gravity does exist on such a hypersurface. We do so by investigating when a certain affine length function associated with any null section is finite and continuous.</p>

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On the existence of null sections with constant surface gravity on non-smooth null hypersurfaces

  • 期刊论文

  • 发表日期：

    2025年10月24日

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  • Ivan P. Costa e Silva,
  • José L. Flores,
  • Benjamín Olea

摘要

We extend the notion of surface gravity to a wide class of non-smooth null hypersurfaces in a spacetime of arbitrary dimension. The lower differentiability presents a number of new challenges, since nearly all the the standard techniques applicable to \(C^k\) C k null hypersurfaces with \(k\ge 2\) k ≥ 2 fail in that context. Nevertheless, we are able to obtain suitable geometric conditions under which a continuous null section with constant surface gravity does exist on such a hypersurface. We do so by investigating when a certain affine length function associated with any null section is finite and continuous.