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.

We construct solutions for thin black rings in Anti-deSitter and deSitter spacetimes using approximate methods. Black rings in AdS exist with arbitrarily large radius and satisfy a bound |J| ≤ LM , which they saturate as their radius becomes infinitely large. For angular momentum near the maximum, they have larger area than rotating AdS black holes. Thin black rings also exist in deSitter space, with rotation velocities varying between zero and a maximum, and with a radius that is always strictly below the Hubble radius. Our general analysis allows us to include black Saturns as well, which we discuss briefly. We present a simple physical argument why supersymmetric AdS black rings must not be expected: they do not possess the necessary pressure to balance the AdS potential. We discuss the possible existence or absence of 'large AdS black rings' and their implications for a dual hydrodynamic description. An analysis of the physical properties of rotating AdS black holes is also included.

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...

We show by explicit computations that the product of all the horizon areas is independent of the mass, regardless of the topology of the horizons. The universal character of this relation holds for all known five dimensional asymptotically flat black rings, and for black strings. This gives further evidence for the crucial role that the thermodynamic properties at each horizon play in understanding the entropy at the microscopic level. To this end we propose a "first law" for the inner Cauchy horizons of black holes. The validity of this formula, which seems to be universal, was explicitly checked in all cases.

The analytic structure of solutions to the Klein-Gordon equation in a black hole background, as represented by monodromy data, is intimately related to black hole thermodynamics. It encodes the "hidden conformal symmetry" of a non-extremal black hole, and it explains why features of the inner event horizon appear in scattering data such as greybody factors. This indicates that hidden conformal symmetry is generic within a universality class of black holes.

We study scattering coefficients in black hole spacetimes using analytic properties of complexified wave equations. For a concrete example, we analyze the singularities of the Teukolsky equation and relate the corresponding monodromies to scattering data. These techniques, valid in full generality, provide insights into complex-analytic properties of greybody factors and quasinormal modes. This leads to new perturbative and numerical methods which are in good agreement with previous results.

There is an exciting prospect of obtaining the shadow of astrophysical black holes (BHs) in the near future with the Event Horizon Telescope. As a matter of principle, this justifies asking how much one can learn about the BH horizon itself from such a measurement. Since the shadow is determined by a set of special photon orbits, rather than horizon properties, it is possible that different horizon geometries yield similar shadows. One may then ask how sensitive is the shadow to details of the horizon geometry? As a case study, we consider the double Schwarzschild BH and analyse the impact on the lensing and shadows of the conical singularity that holds the two BHs in equilibrium -herein taken to be a strut along the symmetry axis in between the two BHs. Whereas the conical singularity induces a discontinuity of the scattering angle of photons, clearly visible in the lensing patterns along the direction of the strut's location, it produces no observable effect on the shadows, whose edges remain everywhere smooth. The latter feature is illustrated by examples including both equal and unequal mass BHs. This smoothness contrasts with the intrinsic geometry of the (spatial sections of the) horizon of these BHs, which is not smooth, and provides a sharp example on how BH shadows are insensitive to some horizon geometry details. This observation, moreover, suggests that for the study of their shadows, this static double BH system may be an informative proxy for a dynamical binary.

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