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

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