Non-commutative Einstein equations and Seiberg-Witten map

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.

6 and 1/2 pages, based on talk prepared for the Friedmann Seminar, May-June 2011. In the final version, the presentation has been improved, including a better notation

References in corpus (4)

• Noncommutative Gravity Solutions
• Exact Black Hole Solutions in Noncommutative Gravity
• Notes on "quantum gravity" and non-commutative geometry
• SL(2,C) gravity on noncommutative space with Poisson structure

Cited by in corpus (6)

• Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map
• Gauge theories on quantum spaces
• Non-commutative black holes of various genera in the connection formalism
• Self-dual road to noncommutative gravity with twist: a new analysis
• Some singular spacetimes and their possible alternatives
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly