The asymptotic of static isolated systems and a generalised uniqueness for Schwarzschild

TL;DR

This paper proves that static, spacetime-geodesically complete systems with certain topologies are asymptotically flat without energy conditions, and generalizes the Schwarzschild uniqueness theorem beyond asymptotic flatness.

Contribution

It introduces a broad generalization of Schwarzschild uniqueness, removing the need for asymptotic flatness and establishing asymptotic flatness under minimal assumptions.

Findings

Static systems with specified topology are asymptotically flat.

The generalization of Schwarzschild uniqueness does not require asymptotic flatness.

The Korotkin-Nicolai black hole exemplifies the optimality of the hypotheses.

Abstract

It is proved that any static system that is spacetime-geodesically complete at infinity, and whose spacelike-topology outside a compact set is that of R^3 minus a ball, is asymptotically flat. The matter is assumed compactly supported and no energy condition is required. A similar (though stronger) result applies to black holes too. This allows us to state a large generalisation of the uniqueness of the Schwarzschild solution not requiring asymptotic flatness. The Korotkin-Nicolai static black-hole shows that, for the given generalisation, no further flexibility in the hypothesis is possible.