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A generalized set of asymptotic conditions for higher spin gravity withoutcosmological constant in three spacetime dimensions is constructed. Theyinclude the most general temporal components of the gauge fields thatmanifestly preserve the original asymptotic higher spin extension of theBMS$_{3}$ algebra, with the same central charge. By virtue of a suitablepermissible gauge choice, it is shown that this set can be directly recoveredas a limit of the boundary conditions that have been recently constructed inthe case of negative cosmological constant, whose asymptotic symmetries arespanned by two copies of the centrally-extended W$_{3}$ algebra. Since thegeneralized asymptotic conditions allow to incorporate chemical potentialsconjugated to the higher spin charges, a higher spin extension of locally flatcosmological spacetimes becomes naturally included within the set. It is shownthat their thermodynamic properties can be successfully obtained exclusively interms of gauge fields and the topology of the Euclidean manifold, which isshown to be the one of a solid torus, but with reversed orientation as comparedwith one of the black holes. It is also worth highlighting that regularity ofthe fields can be ensured through a procedure that does not require an explicitmatrix representation of the entire gauge group. In few words, we show that thetemporal components of generalized dreibeins can be consistently gauged away,which partially fixes the chemical potentials, so that the remaining conditionscan just be obtained by requiring the holonomy of the generalized spinconnection along a thermal circle to be trivial. The extension of thegeneralized asymptotically flat behaviour to the case of spins $s\geq2$ is alsodiscussed.

Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics