A four-parameter capped black hole solution in 5D minimal supergravity exhibits two branches with identical conserved charges, demonstrating non-uniqueness for spherical black holes.
Entropy of Non-Extreme Charged Rotating Black Holes in String Theory
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abstract
We give the explicit expression for four-dimensional rotating charged black hole solutions of N=4 (or N=8) superstring vacua, parameterized by the ADM mass, four charges (two electric and two magnetic charges, each arising from a different U(1) gauge factors), and the angular momentum (as well as the asymptotic values of four toroidal moduli of two-torus and the dilaton-axion field). The explicit form of the thermodynamic entropy is parameterized in a suggestive way as a sum of the product of the `left-moving' and the `right-moving' terms, which may have an interpretation in terms of the microscopic degrees of freedom of the corresponding D-brane configuration. We also give an analogous parameterization of the thermodynamic entropy for the recently obtained five-dimensional rotating charged black holes parameterized by the ADM mass, three U(1) charges and two rotational parameters (as well as the asymptotic values of one toroidal modulus and the dilaton).
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Nonuniqueness of capped black holes: large and small bubbles
A four-parameter capped black hole solution in 5D minimal supergravity exhibits two branches with identical conserved charges, demonstrating non-uniqueness for spherical black holes.