Resumen de Structure of globally hyperbolic spacetimes-with-timelike-boundary

Luis Alberto Aké Hau, José Luis Flores , Miguel Sánchez Caja

• 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.