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• W2563304057 abstract "Within the generic null characteristic initial value problem a reduced set of the evolution equations are deduced from the coupled Newman–Penrose and Maxwell equations for smooth four-dimensional electrovacuum spacetimes allowing a non-zero cosmological constant. It is shown that these reduced equations make up a first-order symmetric hyperbolic system of evolution equations, and also that the solutions to this reduced system are also solutions to the full set of the Newman–Penrose and Maxwell equations provided that the inner equations hold on the initial data surfaces. The derived generic results are applied in carrying out the investigation of electrovacuum spacetimes distinguished by the existence of a pair of null hypersurfaces, H1 and H2, generated by expansion and shear-free geodesically complete null congruences such that they intersect on a two-dimensional spacelike surface, Z = H1 ∩ H2. Besides the existence of this pair of null hypersurfaces, no assumption concerning the asymptotic structure is made. It is shown that both the spacetime geometry and the electromagnetic field are uniquely determined, in the domain of dependence of H1 ∪ H2 once a complex vector field ξ A (determining the metric induced on Z), the τ spin coefficient and the φ1 electromagnetic potential are specified on Z. The existence of a Killing vector field—with respect to which the null hypersurfaces H1 and H2 comprise a bifurcate-type Killing horizon—is also justified in the domain of dependence of H1 ∪ H2. Since, in general, the freely specifiable data on Z do not have any sort of symmetry, the corresponding spacetimes do not possess any symmetry in addition to the horizon Killing vector field. Thereby, they comprise the class of generic ‘stationary’ distorted electrovacuum black hole spacetimes which for the case of a positive cosmological constant may also (or, in certain cases, only) contain a distorted de Sitter-type cosmological horizon to which our results equally apply. It is also shown that there are stationary distorted electrovacuum black hole configurations such that parallelly propagated curvature blow-up occurs both to the future and to the past ends of some of the null generators of their bifurcate Killing horizon, and also that this behavior is universal. In particular, it is shown that in the space of vacuum solutions to Einstein’s equations, in" @default.
• W2563304057 created "2017-01-06" @default.
• W2563304057 creator A5045987257 @default.
• W2563304057 date "2014-01-01" @default.
• W2563304057 modified "2023-09-24" @default.
• W2563304057 title "Stationary black holes as holographs II" @default.
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