Einstein-Klein-Gordon Research Articles

On further generalization of the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon

A rigidity theorem that applies to smooth electrovacuum spacetimes which represent either (A) an asymptotically flat stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics was given in a recent paper by Friedrich et al (1999 Commun. Math. Phys. 204 691-707). Here we enlarge the framework of the corresponding investigations by allowing the presence of other types of matter fields. In the first part the matter fields are involved merely implicitly via the assumption that the dominant energy condition is satisfied. In the second part Einstein-Klein-Gordon (EKG), Einstein-[non-Abelian]-Higgs (E[nA]H), Einstein-[Maxwell]-Yang-Mills-dilaton (E[M]YMd) and Einstein-Yang-Mills-Higgs (EYMH) systems are studied. The black hole event horizon or, respectively, the compact Cauchy horizon of the considered spacetimes is assumed to be a smooth non-degenerate null hypersurface. It is proved that there exists a Killing vector field in a one-sided neighbourhood of the horizon in EKG, E[nA]H, E[M]YMd and EYMH spacetimes. This Killing vector field is normal to the horizon, moreover, the associated matter fields are also shown to be invariant with respect to it. The presented results provide generalizations of the rigidity theorems of Hawking (for case A) and of Moncrief and Isenberg (for case B) and, in turn, they strengthen the validity of both the black hole rigidity scenario and the strong cosmic censor conjecture of classical general relativity.

Quantum Models for the Lowest-Order Velocity-Dominated Solutions of Irrotational Dust Cosmologies

The lowest-order velocity-dominated solutions to the Einstein dust equations of Eardley, Liang, and Sachs are quantized using the canonical methods of DeWitt and of Arnowitt, Deser, and Misner. The quantum dynamics of these models is shown to be governed by the Einstein-Klein-Gordon (EKG) equation. Exact solutions of the decoupled EKG equations in the discrete limit are obtained, which have the striking feature that the state amplitude vanishes at the singularity for anisotropic models. The geometry of the manifold of the classical 3-metrics is studied and it turns out to be composed of conformally flat geodesic submanifolds. Other difficulties related to the quantum theory such as factor ordering, divergence, interpretation of the volume measure, etc. are also discussed.