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arXiv · 1005.0499

Schwarzschild Geometry Emerging from Matrix Models

Daniel N. Blaschke·Harold Steinacker
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Abstract

We demonstrate how various geometries can emerge from Yang-Mills type matrix models with branes, and consider the examples of Schwarzschild and Reissner-Nordstroem geometry. We provide an explicit embedding of these branes in R^{2,5} and R^{4,6}, as well as an appropriate Poisson resp. symplectic structure which determines the non-commutativity of space-time. The embedding is asymptotically flat with asymptotically constant θ^{μν} for large r, and therefore suitable for a generalization to many-body configurations. This is an illustration of our previous work arXiv:1003.4132, where we have shown how the Einstein-Hilbert action can be realized within such matrix models.

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Daniel N. Blaschke, Harold Steinacker. 2010-05-04. Schwarzschild Geometry Emerging from Matrix Models. https://doi.org/10.1088/0264-9381%2F27%2F18%2F185020

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