Schwarzschild Geometry Emerging from Matrix Models

Details Schwarzschild Geometry Emerging from Matrix Models Schwarzschild Geometry Emerging from Matrix Models

2010-05-04

arxiv.org/abs/1005.0499v1

Class. Quantum Grav. 27:185020, 2010; Class.Quant.Grav.27:185020,2010

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, 1 figure

Scientific paper

10.1088/0264-9381/27/18/185020

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 \theta^{\mu\nu} 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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