Hiroshi Isono, Dan Tomino
Published 2009-11-10, updated 2010-05-03Version 3
Large N matrices can describe covariant derivatives in curved space. Applying this interpretation to the IKKT matrix model, the field equation of gravity is derived from the matrix equation of motion. We study classical solutions of this field equation with torsion degrees of freedom in empty spacetime. Time dependent solutions with homogeneity and isotropy, and time independent solutions with spherical symmetry are investigated under particular settings of torsions.
Comments: 18 pages, 5 figures. v2: one reference and a comment added in section 5, typos corrected. v3: a minor change of the title, explanations of the Bianchi identities added in section 2 and appendix, wording and typos corrected.
Journal: Phys.Rev.D.81,084049 (2010)
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