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General relativistic analog solutions for Yang-Mills theory

Finding solutions to non-linear field theories, such as Yang-Mills theories or general relativity, is usually difficult. The field equations of Yang-Mills theories and general relativity are known to share some mathematical similarities, and this connection can be used to find solutions to one theory using known solutions of the other theory. For example, the Schwarzschild solutions of general relativity can be shown to have a mathematically similar counterpart in Yang-Mills theory. In this article we will discuss several solutions to the Yang-Mills equations which can be found using this connection between general relativity and Yang-Mills theory. Some comments about the possible physical meaning of these solutions will be discussed. In particular it will be argued that some of these analog solutions of Yang-Mills theory may have some connection with the confinement phenomenon. To this end we will briefly look at the motion of test particles moving in the background potential of the Schwarzschild analog solution.