Entropy of Non-Extreme Charged Rotating Black Holes in String Theory

TL;DR

The paper provides explicit classical solutions for non-extreme rotating black holes in N=4 (or N=8) string vacua, detailing four-charge four-dimensional and three-charge five-dimensional configurations. It furnishes the Bekenstein-Hawking entropy in a form that naturally splits into left-moving and right-moving contributions, highlighting the role of angular momentum in the four-dimensional case and drawing parallels to D-brane microstate counting. By employing solution-generating techniques via boosts and leveraging duality symmetries, the authors connect these macroscopic entropies to potential microscopic interpretations on the D-brane world-volume. The work strengthens the link between rotating black holes in string theory and their D-brane descriptions, suggesting symmetric charge-decomposition structures and offering a framework for future microscopic entropy calculations. Overall, it advances understanding of how classical black hole thermodynamics in string theory aligns with D-brane microphysics and duality mappings.

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).