Structure of globally hyperbolic spacetimes-with-timelike-boundary

• Luis Aké Hau ^[1] ; José Luis Flores Dorado ^[2] ; Miguel Sánchez Caja ^[3]
  1. [1] Universidad Autónoma de Yucatán

     Universidad Autónoma de Yucatán

     México

     
  2. [2] Universidad de Málaga

     Universidad de Málaga

     Málaga, España

     
  3. [3] Universidad de Granada

     Universidad de Granada

     Granada, España

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 1, 2021, págs. 45-94
• Idioma: inglés
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• Resumen

  • Globally hyperbolic spacetimes-with-timelike-boundary (M¯¯¯¯¯=M∪∂M,g) are the natural class of spacetimes where regular boundary conditions (eventually asymptotic, if ∂M is obtained by means of a conformal embedding) can be posed. ∂M represents the naked singularities and can be identified with a part of the intrinsic causal boundary. Apart from general properties of ∂M, the splitting of any globally hyperbolic (M¯¯¯¯¯,g) as an orthogonal product R×Σ¯ with Cauchy slices-with-boundary {t}×Σ¯ is proved. This is obtained by constructing a Cauchy temporal function~τ with gradient ∇τ tangent to ∂M on the boundary. To construct such a~τ, results on stability of both global hyperbolicity and Cauchy temporal functions are obtained. Apart from having their own interest, these results allow us to circumvent technical difficulties introduced by ∂M. The techniques also show that M¯¯¯¯¯ is isometric to the closure of some open subset in a globally hyperbolic spacetime (without boundary). As a trivial consequence, the interior M both splits orthogonally and can be embedded isometrically in some LN, extending so properties of globally spacetimes without boundary to a class of causally continuous ones.