Non-commutative Einstein equations and Seiberg-Witten map

TL;DR

This paper investigates the first-order non-commutative Einstein equations derived via the Seiberg--Witten map, focusing on their solutions in Schwarzschild geometry, and explores the map's potential to generate solutions in non-commutative gravity.

Contribution

It extends the application of the Seiberg--Witten map to first-order non-commutative Einstein equations and examines their solutions in Schwarzschild spacetime.

Findings

Seiberg--Witten map can be applied to first-order non-commutative gravity equations.

Solutions in Schwarzschild geometry are analyzed for compatibility with non-commutative corrections.

The study provides insights into the structure of non-commutative Einstein equations and their classical limits.

Abstract

The Seiberg--Witten map is a powerful tool in non-commutative field theory, and it has been recently obtained in the literature for gravity itself, to first order in non-commutativity. This paper, relying upon the pure-gravity form of the action functional considered in Ref. 2, studies the expansion to first order of the non-commutative Einstein equations, and whether the Seiberg--Witten map can lead to a solution of such equations when the underlying classical geometry is Schwarzschild.