Quasilocal non-equilibrium dynamics of Φ-spinning black rings

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In this work, we study the non-equilibrium dynamics of Φ-spinning black rings within the quasilocal formalism. We adopt the counterterm method and compute the renormalized boundary stress-energy tensor. By considering the conservation of this tensor, the condition for removing the conical singularity at spatial infinity is derived. It is subsequently shown that a Φ-spinning black ring cannot be kept in a state of equilibrium, which is consistent with the physical interpretation that the angular momentum is on the plane orthogonal to the ring and there is no force to balance the tension and gravitational self-attraction. The results of these computations lay a foundation for studying the thermodynamics of Φ-spinning rings in detail. Finally, we charge up the rings in Einstein-Maxwell-dilaton system and suggest feasible ways to make them balanced.