Microstates of a Neutral Black Hole in M Theory

TL;DR

The paper investigates neutral five-dimensional Kaluza-Klein black holes in M theory on T^6, which relate to extremal Myers–Perry black holes in the appropriate limit. By mapping to D0–D6 brane configurations in IIA and performing three T-dualities, the authors construct a weakly coupled D-brane description in terms of intersecting D3-branes that exactly reproduces the extremal black hole entropy and mass, despite broken supersymmetry. The key result is that the microscopic count from D3-brane intersections yields S = 2π sqrt{ (N_0^2 N_6^2)/4 − J^2 }, matching the gravitational entropy for generic angular momenta, including unequal charges. This suggests that neutral black holes may admit tractable microscopic descriptions and motivates extensions to near-extremal regimes and broader compactifications.

Abstract

We consider vacuum solutions in M theory of the form of a five-dimensional Kaluza-Klein black hole cross T^6. In a certain limit, these include the five-dimensional neutral rotating black hole (cross T^6). From a IIA standpoint, these solutions carry D0 and D6 charges. We show that there is a weakly coupled D-brane description which precisely reproduces the Hawking-Bekenstein entropy in the extremal limit, even though supersymmetry is completely broken.

Figures (2)

• Figure 1: Branes wrapping the diagonals of a torus. There are two intersection points, at the origin and at the middle of the square. We assume that each intersection contributes a microscopic entropy equal to that of a supersymmetric intersection of branes.
• Figure 2: Generalization to unequal charges and non-trivial moduli. The branes wrap a rational direction $k/l$ of the torus (in the figure, $k=3$, $l=1$), so there are $2kl$ intersection points on each $T^2$. In the limit to the five-dimensional Myers-Perry black hole, the torus shrinks along $x_{2}$.