Schwarzschild geometry emerging from matrix models

Daniel N Blaschke (1) , Harold Steinacker (1)

1 Faculty of Physics [Vienna]

We demonstrate how various geometries can emerge from Yang-Mills type matrix models with branes, and consider the examples of Schwarzschild and Reissner-Nordström 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 [ 1 ], where we have shown how the Einstein-Hilbert action can be realized within such matrix models.

Mots clés: Physical Sciences

Daniel N Blaschke, Harold Steinacker. Schwarzschild geometry emerging from matrix models. Classical and Quantum Gravity, 2010, 27 (18), pp.185020. ⟨10.1088/0264-9381/27/18/185020⟩. ⟨hal-00625166⟩