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<p>In this work we study the structure of the future causal completion <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\hat{M}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>M</mi> <mo stretchy="false">^</mo> </mover> </math></EquationSource> </InlineEquation> of a globally hyperbolic GRW spacetime <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {R}\times _\alpha M\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">R</mi> <msub> <mo>×</mo> <mi>α</mi> </msub> <mi>M</mi> </mrow> </math></EquationSource> </InlineEquation> using the novel notion of Lorentzian pre-length spaces. As our main result, we prove that the causal completion of a GRW spacetime is a globally hyperbolic pre-length space provided the chronological topology is Hausdorff.</p>

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The causal structure of the c-completion of warped spacetimes

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Luis Aké Hau,
  • Saul Burgos,
  • Didier A. Solis

摘要

In this work we study the structure of the future causal completion \(\hat{M}\) M ^ of a globally hyperbolic GRW spacetime \(\mathbb {R}\times _\alpha M\) R × α M using the novel notion of Lorentzian pre-length spaces. As our main result, we prove that the causal completion of a GRW spacetime is a globally hyperbolic pre-length space provided the chronological topology is Hausdorff.