Schwarzschild Geometry Emerging from Matrix Models

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.

21 pages, 1 figure

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Cited by in corpus (13)

• Matrix Model Approach to Cosmology
• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
• Multi-matrix models at general coupling
• On the Phase Structure of Commuting Matrix Models
• Near commuting multi-matrix models
• Thermofield dynamics and Gravity
• On Poisson geometries related to noncommutative emergent gravity
• Scalar modes and the linearized Schwarzschild solution on a quantized FLRW space-time in Yang-Mills matrix models
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Special Geometries Emerging from Yang-Mills Type Matrix Models
• Fuzzy Schwarzschild (2+1)-spacetime
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry I: A QM/NCG Correspondence
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry II: Noncommutative Quantum Black Holes