Black Rings with Varying Charge Density

TL;DR

This paper presents new five-dimensional supersymmetric black ring solutions in M-theory with arbitrary charge density fluctuations, introducing classical moduli that affect entropy and revealing rich horizon symmetries.

Contribution

It introduces the first solutions where black ring entropy depends on classical charge density moduli, with arbitrary fluctuating charge distributions and novel symmetry properties.

Findings

Entropy varies continuously with charge distribution fluctuations.

Existence of solutions with rotationally invariant horizons but broken overall rotational symmetry.

Horizon area defines a Lorentz metric on classical excitations, constrained by Virasoro conditions.

Abstract

We find the general five-dimensional, supersymmetric black ring solutions in M-theory based upon a circular ring, but with arbitrary, fluctuating charge distributions around the ring. The solutions have three arbitrary charge distribution functions, but their asymptotic charges and angular momenta only depend upon the total charges on the ring. The arbitrary density fluctuations thus represent "hair." By varying the charge distributions one can continuously change the entropy of these black rings; to our knowledge this is the first solution in which the entropy depends on classical moduli. We also show that there is a family of solutions, with two arbitrary functions, for which the horizon remains rotationally invariant, and yet the complete solution breaks rotational symmetry. If the horizon area is set to zero then one obtains families of supertube solutions. We find that our general solutions are governed by three harmonic functions that may be thought of as classical excitations of a string. The horizon area provides a natural Lorentz metric on these excitations, and the constancy of the rotational invariance of the horizon imposes a set of Virasoro constraints.