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<p>We obtain new uniqueness results for stochastically complete spacelike hypersurfaces with constant mean curvature in a Lorentzian spacetime that admits a globally defined causal Killing vector field and obeys the Timelike Convergence Condition. These models include the relevant families of stationary and Brinkmann spacetimes. In addition, we sharpen our rigidity result for Einstein’s static universe.</p>

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Stochastically Complete Spacelike Hypersurfaces in Symmetric Spacetimes

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • María Á. Medina,
  • José A. S. Pelegrín

摘要

We obtain new uniqueness results for stochastically complete spacelike hypersurfaces with constant mean curvature in a Lorentzian spacetime that admits a globally defined causal Killing vector field and obeys the Timelike Convergence Condition. These models include the relevant families of stationary and Brinkmann spacetimes. In addition, we sharpen our rigidity result for Einstein’s static universe.