Doubly Spinning Black Rings

Abstract

We study a method to solve stationary axisymmetric vacuum Einstein equations numerically. As an illustration, the five-dimensional doubly spinning black rings that have two independent angular momenta are formulated in a way suitable for fully nonlinear numerical method. Expanding for small second angular velocity, the formulation is solved perturbatively upto second order involving the backreaction from the second spin. The obtained solutions are regular without conical singularity, and the physical properties are discussed with the phase diagram of the reduced entropy vs the reduced angular momenta. Possible extensions of the present approach to constructing the higher dimensional version of black ring and the ring with the cosmological constant are also discussed.

20 pages, 6 figures

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• Black Saturn
• Bicycling Black Rings
• The Black Di-Ring: An Inverse Scattering Construction
• On Hawking radiation from black rings
• $d\ge 5$ static black holes with $S^2\times S^{d-4}$ event horizon topology
• Harrison transformation and charged black objects in Kaluza-Klein theory
• Black Objects and Hoop Conjecture in Five-dimensional Space-time