Construction of unshielded singular solutions of the harmonic field equations

Abstract

Singular solutions of the harmonic Einstein evolution equation are constructed which are related to spatially global and time-local solutions for a certain class of quasilinear hyperbolic systems of second order. The constructed singularities of curvature invariants occur generically and are accessible by g.a.p. curves. The singularities are not strongly censored, and for strongly asymptotically predictable space-times, they are located in the causal past of the future null infinity, and are, hence, not shielded by a black hole. This is an alternative construction of singularities, which may be applied to other hyperbolic equations such as the Euler equation (cf. [3] for a different construction method- both of our constructions are fundamentally different from supercritical blow-up constructions in the Katz-Pavlovic model or singular solution constructions for heat-flow maps in specific dimensions).