General Relativity and Gravitation

, Volume 41, Issue 6, pp 1407–1435 | Cite as

Kinematics in matrix gravity

  • Ivan G. Avramidi
  • Guglielmo Fucci
Research Article


We develop the kinematics in Matrix Gravity, which is a modified theory of gravity obtained by a non-commutative deformation of General Relativity. In this model the usual interpretation of gravity as Riemannian geometry is replaced by a new kind of geometry, which is equivalent to a collection of Finsler geometries with several Finsler metrics depending both on the position and on the velocity. As a result the Riemannian geodesic flow is replaced by a collection of Finsler flows. This naturally leads to a model in which a particle is described by several mass parameters. If these mass parameters are different then the equivalence principle is violated. In the non-relativistic limit this also leads to corrections to the Newton’s gravitational potential. We find the first and second order corrections to the usual Riemannian geodesic flow and evaluate the anomalous nongeodesic acceleration in a particular case of static spherically symmetric background.


Matrix gravity Non-commutative general relativity Non-geodesic motion 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.New Mexico Institute of Mining and TechnologySocorroUSA

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