Electrovacuum Near-horizon Geometries in Four and Five Dimensions

Associated to every stationary extremal black hole is a unique near-horizon geometry, itself a solution of the field equations. These latter spacetimes are more tractable to analyze and most importantly, retain properties of the original black hole which are intrinsic to the event horizon. After reviewing general features of near-horizon geometries, such as SO(2,1) symmetry enhancement, I report on recent work on stationary, charged extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions and present a classification of near-horizon geometries of black holes on this kind. In five dimensions, charged extremal black hole solutions to minimal (gauged) supergravity, which arises naturally in string theory and the gauge theory/gravity correspondence, are considered. I consider the classification of near-horizon geometries for the subset of such black holes which are supersymmetric. Recent progress on the classification problem in the general extremal, non-supersymmetric case is also discussed.Comment: Invited contribution to a special issue of Classical and Quantum Gravity on the 19th International Conference on General Relativity and Gravitation, Mexico City, July 5-9, 201

Constructing near-horizon geometries in supergravities with hidden symmetry

We consider the classification of near-horizon geometries in a general two-derivative theory of gravity coupled to abelian gauge fields and uncharged scalars in four and five dimensions, with one and two commuting rotational symmetries respectively. Assuming that the theory of gravity reduces to a 3d non-linear sigma model (as is typically the case for ungauged supergravities), we show that the functional form of any such near-horizon geometry may be determined. As an example we apply this to five dimensional minimal supergravity. We also construct an example of a five parameter near-horizon geometry solution to this theory with S^1 X S^2 horizon topology. We discuss its relation to the near-horizon geometries of the yet to be constructed extremal black rings with both electric and dipole charges.Comment: Latex, 30 pages. v2: discussion in section 5 modified and improved, other minor changes, references adde

Involvement of CytochromeP4504a in Adenosine A1 receptor mediated regulation of vascular tone

Cardiovascular diseases are one of the leading causes of morbidity and mortality worldwide. The regulation of vascular tone plays an important role in normal cardiovascular function. Adenosine, an autacoid has several physiological and pathophysiological roles, apart from the regulation of vascular tone. Adenosine receptor (AR) contracts and relaxes blood vessels through all four subtypes (A1, A2A, A2B, and A3) linked to different signaling mechanisms. Deciphering complex tissue responses remains difficult because relationships of individual receptor subtypes and various end-effectors (e.g., ion channels) are yet to be identified. Apart from adenosine, 20-HETE, a cytochrome P4504a (Cyp4a) metabolite of arachidonic acid (AA) is a potent vasoconstrictor.;We hypothesized that A1AR induced contraction of the smooth muscle involves Cyp4a, with Protein Kinase C (PKC)-alpha, extracellular regulated kinase (ERK) 1/2 contributing to the downstream signaling events. Another key question we addressed were the ion channel(s) contributing to smooth muscle contraction. Experiments included isometric tension recordings of aortic contraction and western blots. In addition, patch clamp experiments were done with freshly isolated smooth muscle cells from wild type (WT) and A1 knockout (A1KO) mice aortae. We found that inhibition of Cyp4a led to lesser contraction in the adenosine agonists\u27 mediated responses. 20-HETE induced contraction in both WT and A1KO, but this response was lower in A1KO. Inhibition of PKC-alpha and ERK1/2 attenuated the 20-HETE-induced contraction in both WT and A1KO. These findings suggest that A1AR couples with 20-HETE and negatively modulates vascular tone through PKC-alpha and ERK1/2. Furthermore, electrophysiological experiments revealed that non-selective adenosine agonist increased the BK current in A1KO as compared to the WT. This suggests A1 receptors have a negative regulatory effect on BK current. On the other hand, A1 selective agonist decreased the BK current in WT, with no effect on A1KO. PKC-alpha inhibitor abolished the effect of the A 1 selective agonist on BK current. These findings suggest that A 1AR regulates contraction of the aortic smooth muscle through inhibition of BK channels in a PKC-alpha dependent manner. From these data, we conclude that A1AR negatively couples with 20-HETE and by inhibiting BK channels mediates smooth muscle contraction via PKC-alpha

Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes

We consider stationary extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions. We determine all non-static axisymmetric near-horizon geometries (with non-toroidal horizon topology) and all static near-horizon geometries for black holes of this kind. This allows us to deduce that the most general near-horizon geometry of an asymptotically globally AdS(4) rotating extremal black hole, is the near-horizon limit of extremal Kerr-Newman-AdS(4). We also identify the subset of near-horizon geometries which are supersymmetric. Finally, we show which physical quantities of extremal black holes may be computed from the near-horizon limit alone, and point out a simple formula for the entropy of the known supersymmetric AdS(4) black hole. Analogous results are presented in the case of vanishing cosmological constant.Comment: 18 pages, Latex. v2: footnote added on pg. 12. v3: assumption of non-toroidal horizon topology made explicit, minor clarification

All Vacuum Near-Horizon Geometries in DD-dimensions with (D−3)(D-3) Commuting Rotational Symmetries

We explicitly construct all stationary, non-static, extremal near horizon geometries in $D$ dimensions that satisfy the vacuum Einstein equations, and that have $D-3$ commuting rotational symmetries. Our work generalizes [arXiv:0806.2051] by Kunduri and Lucietti, where such a classification had been given in $D=4,5$. But our method is different from theirs and relies on a matrix formulation of the Einstein equations. Unlike their method, this matrix formulation works for any dimension. The metrics that we find come in three families, with horizon topology $S^2 \times T^{D-4}$, or $S^3 \times T^{D-5}$, or quotients thereof. Our metrics depend on two discrete parameters specifying the topology type, as well as $(D-2)(D-3)/2$ continuous parameters. Not all of our metrics in $D \ge 6$ seem to arise as the near horizon limits of known black hole solutions.Comment: 22 pages, Latex, no figures, title changed, references added, discussion of the parameters specifying solutions corrected, amended to match published versio

New thermodynamic identities for five-dimensional black holes

We derive new identities for the thermodynamic variables of five-dimensional, asymptotically flat, stationary and biaxisymmetric vacuum black holes. These identities depend on the topology of the solution and include contributions arising from certain topological charges. The proof employs the harmonic map formulation of the vacuum Einstein equations for solutions with these symmetries.Comment: 5 pages. v2: minor edit

Toric Kahler metrics and AdS_5 in ring-like co-ordinates

Stationary, supersymmetric supergravity solutions in five dimensions have Kahler metrics on the four-manifold orthogonal to the orbits of a time-like Killing vector. We show that an explicit class of toric Kahler metrics provide a unified framework in which to describe both the asymptotically flat and asymptotically AdS solutions. The Darboux co-ordinates used for the local description turn out to be ''ring-like.'' We conclude with an Ansatz for studying the existence of supersymmetric black rings in AdS.Comment: A new appendix derives the explicit co-ordinate transformation between the ``ring-like'' co-ordinates and the polar co-ordinates of global AdS. Also, references adde

Do supersymmetric anti-de Sitter black rings exist?

We determine the most general near-horizon geometry of a supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional minimal gauged supergravity that admits two rotational symmetries. The near-horizon geometry is that of the supersymmetric, topologically spherical, black hole solution of Chong et al. This proves that regular supersymmetric anti-de Sitter black rings with two rotational symmetries do not exist in minimal supergravity. However, we do find a solution corresponding to the near-horizon geometry of a supersymmetric black ring held in equilibrium by a conical singularity, which suggests that nonsupersymmetric anti-de Sitter black rings may exist but cannot be "balanced" in the supersymmetric limit.Comment: Latex, 18 pages, 1 figure. v2: minor change

CFT Duals for Extreme Black Holes

It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS black hole is holographically dual to a (chiral half of a) two-dimensional CFT, generalizing an argument given recently for the special case of extremal Kerr. Specifically, the asymptotic symmetries of the near-horizon region of the general extremal black hole are shown to be generated by a Virasoro algebra. Semiclassical formulae are derived for the central charge and temperature of the dual CFT as functions of the cosmological constant, Newton's constant and the black hole charges and spin. We then show, assuming the Cardy formula, that the microscopic entropy of the dual CFT precisely reproduces the macroscopic Bekenstein-Hawking area law. This CFT description becomes singular in the extreme Reissner-Nordstrom limit where the black hole has no spin. At this point a second dual CFT description is proposed in which the global part of the U(1) gauge symmetry is promoted to a Virasoro algebra. This second description is also found to reproduce the area law. Various further generalizations including higher dimensions are discussed.Comment: 18 pages; v2 minor change