Abstract
By employing the new ultraspinning limit we construct novel classes of black holes with non-compact event horizons and finite horizon area and study their thermodynamics. Our ultraspinning limit can be understood as a simple generating technique that consists of three steps: i) transforming the known rotating AdS black hole solution to a special coordinate system that rotates (in a given 2-plane) at infinity ii) boosting this rotation to the speed of light iii) compactifying the corresponding azimuthal direction. In so doing we qualitatively change the structure of the spacetime since it is no longer possible to return to a frame that does not rotate at infinity. The obtained black holes have non-compact horizons with topology of a sphere with two punctures. The entropy of some of these exceeds the maximal bound implied by the reverse isoperimetric inequality, such black holes are super-entropic.
Highlights
Black ring solution of Emparan and Reall which has horizon topology S2 × S1 [2]
Our ultraspinning limit can be understood as a simple generating technique that consists of three steps: i) transforming the known rotating anti de Sitter (AdS) black hole solution to a special coordinate system that rotates at infinity ii) boosting this rotation to the speed of light iii) compactifying the corresponding azimuthal direction
Ultraspinning black holes were first studied by Emparan and Myers [16] in an analysis focusing on the stability of Myers-Perry black holes [17] in the limit of large angular momentum
Summary
In what follows we shall construct new AdS black hole solutions by employing the novel super-entropic ultraspinning limit in which the rotation parameter a attains its maximal value, equal to the AdS radius l. They exceed the maximal entropy bound implied by the reverse isoperimetric inequality To avoid a singular metric in this limit, we need only define a new azimuthal coordinate ψ = φ/Ξ (the metric is already written in coordinates that rotate at infinity) and identify it with period 2π/Ξ to prevent a conical singularity. After this coordinate transformation the a → l limit can be straightforwardly taken and we get the following solution:. This solution was found as a limit of the Carter-Plebanski solution and corresponds to the case where the angular quartic structure function has two double roots [12, 13]
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