Schwarzschild Geometry Emerging from Matrix Models

TL;DR

This paper shows how classical geometries like Schwarzschild and Reissner-Nordstroem can emerge from matrix models, providing explicit embeddings and structures that relate to non-commutative space-time and general relativity.

Contribution

It presents explicit embeddings of Schwarzschild and Reissner-Nordstroem geometries in matrix models, extending previous work on emergent gravity from non-commutative geometry.

Findings

Explicit embeddings of black hole geometries in matrix models

Asymptotically flat embeddings suitable for many-body configurations

Connection to Einstein-Hilbert action within 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 \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.