Black holes analogies in Yang-Mills theory Theory of gravity is very similar to Yang-Mills theory.
In General relativity there are black holes. Is some analogies of black holes in Yang-Mills theory?
 A: There is a recently discovered correspondence between gauge theory and gravity called the double copy, which relates two distinct non-abelian Yang–Mills theories and gravity. Informally, gravity theory can be seen as a “product” of sorts of two gauge theories:
$$ \text{gravity} = \text{gauge} \times \text{gauge}.$$
Originally this correspondence has been formulated at the level of quantum scattering amplitudes but since then it has been extended to include maps relating classical solutions in gauge theories and  in gravity, the so-called classical double copy. For now, this classical correspondence has been established for configurations that linearize the field equations. At the gravity side this include Kerr–Schild metrics:
$$
 g_{μν} = \eta_{μν} + \phi(x) k_μ k_ν,
$$
where $η_{μν}$ is Minkowski spacetime metric, $ϕ$ is the scalar field and $k_μ$ is the null vector field.
At the Yang–Mills side of the correspondence the gauge field would be:
$$
A^{a}_μ = c^a \phi(x) k_μ,
$$
where $c^{a}$ is the color factor while $\phi$ and $k_\mu$ are taken from gravity side.
Since Schwarzschild and Kerr metrics could be written in Kerr–Schild form, this correspondence would be enough to write down the gauge field analogues of static and rotating black holes. For Schwarzschild metric the gauge side is simply the Coulomb field of a color charge. For Kerr black hole the gauge field is sourced by a rotating color charged disk and away from it contains both Coulomb term and magnetic dipole term. A metric with a NUT parameter corresponds to a dyon. Higher dimensional generalizations are also available. All of these examples are Abelian-like (essentially Maxwell fields) in character, though it is conjectured that the correspondence extends to full nonlinear theories.
References
For a pedagogical introduction to the topic:

*

*White, C. D. (2018). The double copy: gravity from gluons. Contemporary Physics, 59(2), 109-125, arXiv:1708.07056.

For more details about black hole analogues in gauge theories:

*

*Monteiro, R., O’Connell, D., & White, C. D. (2014). Black holes and the double copy. Journal of High Energy Physics, 2014(12), 56, doi:10.1007/JHEP12(2014)056, arXiv:1410.0239.

