Analytic meronic black holes, gravitating solitons and higher spins in the Einstein $SU(N)$-Yang-Mills theory

Abstract: We construct meronic black holes and solitons in the Einstein $SU(N)$-Yang-Mills theory in $D=4$ and $D=5$ dimensions. These analytical solutions are found by combining the generalized hedgehog ansatz with the Euler parameterization of the $SU(N)$ group from which the Yang-Mills equations are automatically satisfied for all values of $N$ while the Einstein equations can be solved analytically. We explicitly show the role that the color number $N$ plays in the black hole thermodynamics as well as in the gravitational spin from isospin effect. Two remarkable results of our analysis are that, firstly, meronic black holes can be distinguished by colored black holes by looking at the spin from isospin effect (which is absent in the latter but present in the former). Secondly, using the theory of non-embedded ansatz for $SU(N)$ together with the spin from isospin effect, one can build fields of arbitrary high spin out of scalar fields charged under the gauge group. Hence, one can analyze interacting higher spin fields in asymptotically flat space-times without "introducing by hand" higher spin fields. Our analysis also discloses an interesting difference between the spin from isospin effect in $D=4$ and in $D=5$.