Numerical analysis of 5D indices shows a transition from BMPV black hole entropy to black ring entropy at critical angular momentum m, while PT invariants exhibit two further transitions at positive m and DT invariants transition to D0-brane dominance.
Microscopic Entropy of the Black Ring
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abstract
A surprising new seven-parameter supersymmetric black ring solution of five-dimensional supergravity has recently been discovered. In this paper, M-theory is used to give an exact microscopic accounting of its entropy.
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Large Order Enumerative Geometry, Black Holes and Black Rings
Numerical analysis of 5D indices shows a transition from BMPV black hole entropy to black ring entropy at critical angular momentum m, while PT invariants exhibit two further transitions at positive m and DT invariants transition to D0-brane dominance.