Black rings in large D membrane paradigm at the first order

Black rings are the black objects found in D spacetime dimensional gravity when D >= 5. These have event horizon topology S(D-3)x S-1. In this work the solutions of the large D membrane paradigm dual to stationary black rings in Einstein-Maxwell theory with or without cosmological constant are studied. It is shown that the first order membrane equations can only admit static asymptotically flat black rings, and the equilibrium angular velocity for the asymptotically AdS black rings at large D was obtained. The thermodynamic and dynamic stability of the asymptotically flat black ring solutions is studied. The apparent shortcomings of some of these results are argued to be curable within the large D membrane paradigm framework.

Automated summary

This study examines the solutions of stationary black rings in Einstein-Maxwell theory with or without cosmological constant within the framework of the large D membrane paradigm. It is shown that the first order membrane equations only allow for static asymptotically flat black rings, and the equilibrium angular velocity for asymptotically AdS black rings at large D is obtained. The thermodynamic and dynamic stability of the asymptotically flat black ring solutions is also investigated, with arguments that the apparent shortcomings of some results can be addressed within the large D membrane paradigm framework.