Bicycling black rings

Abstract

We present detailed physics analyses of two different 4+1-dimensional asymptotically flat vacuum black hole solutions with spin in two independent planes: the doubly spinning black ring and the bicycling black ring system ("bi-rings"). The latter is a new solution describing two concentric orthogonal rotating black rings which we construct using the inverse scattering technique. We focus particularly on extremal zero-temperature limits of the solutions. We construct the phase diagram of currently known zero-temperature vacuum black hole solutions with a single event horizon, and discuss the non-uniqueness introduced by more exotic black hole configurations such as bi-rings and multi-ring saturns. IntroductionBlack holes with zero temperature are of considerable interest since one has a good chance of understanding the microscopic origin of their physical properties, such as their entropy. Asymptotically flat supersymmetric black holes fall in this class of solutions, and there has been considerable progress in understanding their properties in string theory since the pioneering work of Strominger and Vafa [1]. Non-supersymmetric extremal black holes with zero temperature are likewise of interest. Recent progress on understanding the microscopic nature of non-supersymmetric zero temperature black holes includes [2,3,4,5,6,7,8].Non-supersymmetric black hole solutions are in general more difficult to work with, not just in terms of understanding their microscopics, but also because they are typically not easy to come by: exact solutions for non-supersymmetric black holes tend to be harder to construct than their supersymmetric cousins. This is in particular true for multi-centered solutions. With their harmonic functions, supersymmetric black holes can easily be superimposed, but non-supersymmetric systems can exhibit strong interactions between the individual black hole components, and the solutions are consequently more involved.Application of integrability methods in higher-dimensional gravity has recently allowed progress on construction of new exact black hole vacuum solutions. For instance, the inverse scattering technique was used in the construction of the first asymptotically flat multi-black hole vacuum solution [9]. The solution -named "black saturn" for its characteristic appearance, a black ring balanced by rotation around a spherical black hole -exhibited clear signs of interactions, including gravitational frame-dragging. Other novel properties included a large degree of continuous non-uniqueness even for zero total angular momentum [9, 10]. The black saturn system, as constructed in [9], did not have a zero temperature limit. However, based on the results found in this paper, we propose the existence of an extremal zero-temperature black saturn solution, and we discuss the consequences of its expected continuous non-uniqueness for the phase diagram of extremal zero-temperature vacuum black holes.In this paper we study two different 4+1-dimensional black hole systems with spin in the two independent p...

Rotating black rings on Taub-NUT

“…From this solution we can also recover the extremal PS black ring [5,26] in the limit when the NUT charge n becomes infinite. This limiting procedure is the same as that for the Class I solution, except that the NUT charge now takes the new value in (4.32).…”

“…In fact, it has been used with much success to generate new black-hole solutions in five dimensions, such as the doubly rotating black ring [5,7], multiple-horizon solutions like the black Saturn [25] and bi-ring [26], as well as black holes on non-trivial gravitational instanton backgrounds [8]. A recent review of some of this progress can be found in [17].…”

“…The extremal PS black ring [5,26] is recovered in the limit when the NUT charge n becomes infinite. More precisely, to take this limit, we first need to perform the following parameter redefinition and coordinate transformations: 10) and then set a → ∞ (after taking out an overall factor 4n).…”

Three-charge supertubes in a rotating black hole background

“…This would be a pair of orthogonal charged black rings in the overspinning case, or a pair of black rings with an additional central black hole in the non-overspinning case. Possible candidates include charged versions of black bi-rings found in [33,34], and the bi-ring black Saturn proposed in [33]. Recent attempts to charge black Saturn, however, have been plagued with singularities [35].…”

Black Holes in Higher-Dimensional Gravity

“…For rotating black holes most progress in recent years has been in five dimensions. Here, it has been found that in addition to the Myers-Perry (MP) black holes [15], there exist rotating black rings [16,2] and multi-black hole solutions like black-Saturns and multi-black rings [17,18,19,20] including those with two independent angular momenta [21,22,23]. All of these are exact solutions which have been obtained with the aid of special ansätze [24,25] based on symmetries and inverse-scattering techniques [26,27,28,29].…”