The existence theorem for the general relativistic Cauchy problem on the light-cone

TL;DR

This paper proves the existence of solutions to the vacuum Einstein equations given initial data on a light-cone, advancing the understanding of the Cauchy problem in general relativity.

Contribution

It establishes the existence theorem for the Einstein equations with initial data specified on a light-cone, a novel geometric setting.

Findings

Existence of vacuum Einstein solutions with light-cone initial data.

Extension of the Cauchy problem to light-cone geometries.

Mathematical framework for solving Einstein equations in this setting.

Abstract

We prove existence of solutions of the vacuum Einstein equations with initial data induced by a smooth metric on a light-cone.