The phase structure of higher-dimensional black rings and black holes

Abstract

We construct an approximate solution for an asymptotically flat, neutral, thin rotating black ring in any dimension D ≥ 5 by matching the near-horizon solution for a bent boosted black string, to a linearized gravity solution away from the horizon. The rotating black ring solution has a regular horizon of topology S 1 × S D−3 and incorporates the balancing condition of the ring as a zero-tension condition. For D = 5 our method reproduces the thin ring limit of the exact black ring solution. For D ≥ 6 we show that the black ring has a higher entropy than the Myers-Perry black hole in the ultraspinning regime. By exploiting the correspondence between ultra-spinning black holes and black membranes on a two-torus, we take steps towards qualitatively completing the phase diagram of rotating blackfolds with a single angular momentum. We are led to propose a connection between MP black holes and black rings, and between MP black holes and black Saturns, through merger transitions involving two kinds of 'pinched' black holes. More generally, the analogy suggests an infinite number of pinched black holes of spherical topology leading to a complicated pattern of connections and mergers between phases.

Thermodynamics of plasmaballs and plasmarings in 3+1 dimensions

“…Nonetheless Emparan and collaborators [1,2] have presented physically motivated conjectures for the structure of these solutions (see also [7] for a perturbative construction of a non uniform black string in AdS 6 ). In this section we will compare the moduli space of solutions obtained in this paper with that conjectured in [1]. We will find some similarities but also other differences.…”

“…The thin line from C to D represents the black ring (with S 3 ⊗ S 1 topology) and the grey thick line from B to C is the conjectured smooth interpolation from the ordinary ball to the ring type through the 'pinched ball' solutions, with the point C being the point of extreme pinching. It is important to note however that the authors in [1] make it clear that this part of the diagram is a guess.…”

“…In section 5 we present a thorough numerical analysis of the thermodynamic properties of the ball and ring solutions, and the resultant phase diagram of the system. in section 6 we compare this phase diagram to the conjectured phase diagram for spinning black holes and black rings in flat space, presented by Emparan and collaborators [1].…”

“…Black holes in dimensions greater than four have recently drawn considerable interest [1][2][3]. They not only provide testing ground of String theory (for example counting of microstates to obtain the entropy) but also are interesting in their own right as they aid the greater understanding of General Relativity.…”

Three-charge supertubes in a rotating black hole background

“…This topic is currently under investigation. A detailed study of this process will have implications for our knowledge of the phase structure of higher dimensional black objects [36,37] in the charged regime. A The general second-order Lagrangian…”