D-branes and spinning black holes

Abstract

We obtain a new class of spinning charged extremal black holes in five dimensions, considered both as classical configurations and in the Dirichlet(D)-brane representation. The degeneracy of states is computed from the D-brane side and the entropy agrees perfectly with that obtained from the black hole side. 2/96♣

One ring to rule them all and in the darkness bind them?

“…Step 1 The first equation to solve is the homogeneous one, (21), which implies that the G i satisfy the Euclidean, vacuum Maxwell equations. Conversely, given a solution, F , to the Maxwell equations one can take G i = F + * F .…”

“…(It is also surprising that the equations that govern the G i are completely independent of the metric coefficients A i !) For the solutions that we seek, the G i are sourced by the dipole M5 branes, and so the G i must fall off suitably fast at infinity, and the location and shape of these branes thus completely determines the solution to (21). Since there are three independent G i 's, there are three independent source distributions to be chosen.…”

“…Section 4 contains explicit solutions that describe supertubes and black rings with three charges, three dipole charges, and U(1) × U(1) symmetry, as well as solutions containing both a BMPV black hole [21] and a black ring. These solutions generalize the three equal-charge BPS black ring solutions constructed in [8] and reduce in the near ring regime to the solutions in [7].…”

New connections between 4D and 5D black holes

“…These are the 5D spinning black holes [4], characterized by membrane charges q A and angular momentum J L associated to the U (1) L isometry. Their characteristic size r BH grows as the square root of the graviphoton charge √ Q which in turn is proportional to the membrane charge q A .…”

“…index) Z should not depend on the radius R, yielding an equality of the form Z 4D = Z 5D with a certain relation between the arguments. The microscopic description for many (but not all) 5D spinning black holes is known [3,4]. Hence this 5D-4D relation gives a microscopic description of 4D black holes for many cases in which it had previously been unknown.…”