A non-existence result for a generalization of the equations of the conformal method in general relativity

TL;DR

This paper demonstrates that a slight modification of the conformal method's equations in general relativity has no solutions for many parameters, indicating the complexity of the original equations' solvability.

Contribution

It proves a non-existence result for a generalized form of the conformal method equations, highlighting the subtlety in their solvability.

Findings

Modified equations admit no solutions for a broad parameter range

Existence of solutions to original equations is more complex than previously thought

Highlights limitations of the conformal method in solving Einstein's constraint equations

Abstract

The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admits no solution for a broad range of parameters. This suggests that the question of existence or non-existence of solutions to the original equations is more subtle than could perhaps be expected.