On smoothness-asymmetric null infinities

TL;DR

This paper explores initial data configurations in vacuum Einstein equations that lead to spacetimes with asymmetric smoothness properties at past and future null infinities, revealing new possibilities for black hole models.

Contribution

It demonstrates how free parameters in conformally flat, axially symmetric initial data can produce spacetimes with asymmetric null infinity smoothness, a novel insight into black hole initial data.

Findings

Existence of initial data with asymmetric null infinity smoothness.

Parameters can be tuned to satisfy smoothness obstructions.

Developments can exhibit peeling future null infinity and non-peeling past null infinity.

Abstract

We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past and a future null infinity of different smoothness. For simplicity, the analysis is restricted to the class of conformally flat, axially symmetric initial data sets. It is shown how the free parameters in the second fundamental form of the data can be used to satisfy certain obstructions to the smoothness of null infinity. The resulting initial data sets could be interpreted as those of some sort of (non-linearly) distorted Schwarzschild black hole. Its developments would be so that they admit a peeling future null infinity, but at the same time have a polyhomogeneous (non-peeling) past null infinity.