Conformal extensions for stationary spacetimes

TL;DR

This paper develops a conformal framework for stationary spacetimes, demonstrating that the cylinder at spatial infinity can be constructed analytically and independently of gauge choices, leading to a well-posed initial value problem.

Contribution

It introduces a gauge-independent method for constructing the cylinder at spatial infinity in stationary spacetimes, ensuring regularity of the initial value problem.

Findings

Tensor fields admit analytic expansions near the cylinder at spatial infinity.

Construction is independent of conformal gauge choice.

Initial value problem for stationary data is as regular as possible.

Abstract

The construction of the cylinder at spatial infinity for stationary spacetimes is considered. Using a specific conformal gauge and frame, it is shown that the tensorial fields associated to the conformal Einstein field equations admit expansions in a neighbourhood of the cylinder at spatial infinity which are analytic with respect to some suitable time, radial and angular coordinates. It is then shown that the essentials of the construction are independent of the choice of conformal gauge. As a consequence, one finds that the construction of the cylinder at spatial infinity and the regular finite initial value problem for stationary initial data sets are, in a precise sense, as regular as they could be.