A Noncommutative Extension of Gravity

Details A Noncommutative Extension of Gravity A Noncommutative Extension of Gravity

1993-07-22

arxiv.org/abs/gr-qc/9307030v1

Int.J.Mod.Phys.D3:221-224,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages. Talk delivered at the 'journ\'ees Relativistes 93'

Scientific paper

10.1142/S0218271894000332

The commutative algebra of functions on a manifold is extended to a noncommutative algebra by considering its tensor product with the algebra of nxn complex matrices. Noncommutative geometry is used to formulate an extension of the Einstein-Hilbert action. The result is shown to be equivalent to the usual Kaluza-Klein theory with the manifold SUn as an internal space, in a truncated approximation.

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