A Dirichlet-type integral on spheres, applied to the fluid/gravity correspondence

We evaluate an analogue of an integral of Dirichlet over the sphere S^D, but with an integrand that is independent of [(D + 1)/2] Killing coordinates. As an application, we evaluate an integral that arises when comparing a conformal fluid on S^D and black holes in (D + 2)-dimensional anti-de Sitter spacetime.Comment: 5 page

Higher-dimensional lifts of Killing-Yano forms with torsion

Using a Kaluza-Klein-type lift, it is shown how Killing-Yano forms with torsion can remain symmetries of a higher-dimensional geometry, subject to an algebraic condition between the Kaluza-Klein field strength and the Killing-Yano form. The lift condition's significance is highlighted, and is satisfied by examples of black holes in supergravity.Comment: 16 pages; v2: lift condition explicitly solve

Conformal isometry of the six-dimensional black string and dualities of null geodesics

We show that the extreme six-dimensional black string admits a conformal isometry under inversion. Duality relations between null geodesics of various brane geometries are demonstrated, some of which have a geometrical origin through an optical metric.Comment: 9 pages. v2: references adde

Characterization of three-dimensional Lorentzian metrics that admit four Killing vectors

We consider three-dimensional Lorentzian metrics that locally admit four independent Killing vectors. Their classification is summarized, and conditions for characterizing them are found. These consist of algebraic classification of the traceless Ricci tensor, and other conditions satisfied by the curvature and its derivative.Comment: 15 page

Isolated poliovirus capsid protein VP1 induces a neutralizing response in rats

Antibodies were raised in rats against the poliovirus type 1 capsid proteins, VP1, VP2, and VP3. Antibodies directed against VP1 from type 1 poliovirus (Mahoney) neutralized type 1 but not type 2 poliovirus. Antibodies raised against VP2 and VP3 failed to neutralize type 1 virus. Thus, VP1 appears to be a neutralizing antigen for poliovirus and in its denatured form presents to the immune system its neutralizing determinants

Two-charge rotating black holes in four-dimensional gauged supergravity

We obtain an asymptotically AdS, non-extremal, electrically charged and rotating black hole solution of 4-dimensional U(1)^4 gauged supergravity with 2 non-zero and independent U(1) charges. The thermodynamical quantities are computed. We find BPS solutions that are nakedly singular. The solution is generalized to include a NUT parameter and dyonic gauge fields. The string frame metric has a rank-2 Killing-Stackel tensor and has completely integrable geodesic motion, and the massless Klein-Gordon equation separates for the Einstein frame metric.Comment: 15 pages; v2, v3: minor change

Black holes in N=8 supergravity from SO(4,4) hidden symmetries

We detail the construction of the most general asymptotically flat, stationary, rotating, non-extremal, dyonic black hole of the four-dimensional N=2 supergravity coupled to 3 vector multiplets that describes the STU model. It generates through U-dualities the most general asymptotically flat, stationary black hole of N=8 supergravity. We develop the solution generating technique based on SO(4,4)/SL(2,R)^4 coset model symmetries, with an emphasis on the 4-fold permutation symmetry of the gauge fields. We indicate how previously known non-extremal and extremal solutions of the STU model are recovered as limiting cases. Several properties of the general black hole solution are discussed, including its thermodynamics, the quadratic mass formula, the Bogomolny-Prasad-Sommerfield limit, the slow and fast extremal rotating limits, its properties in regards to the Kerr/conformal field theory correspondence, its Killing tensors and the separability of geodesic motion and probe scalars.Comment: 63 pages; v2: minor changes, references added; v3: minor changes, published version; v4: minor clarifications and typos fixed, Mathematica file of solution include

Metric transformations under collapsing of Riemannian manifolds

Let (M,g) be a Riemannian manifold with an isometric action of the Lie group G. Let g_G be a left invariant metric on G. Consider the diagonal G action on the product $M \times G$ with the metric g+g_G. In this paper we calculate the formula for the metric h on the quotient space $(M \times G) / G$; the map from g to h is the metric transformation. In particular when g is the hyperbolic metric on H^2 and G=S^1, the transformed metric h is Hamilton's cigar soliton metric studied in the Ricci flow.Comment: 10 pages. This is a revised version with a new reference to previous work of Cheege

Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature

We study sequences of 3-dimensional solutions to the Ricci flow with almost nonnegative sectional curvatures and diameters tending to infinity. Such sequences may arise from the limits of dilations about singularities of Type IIb. In particular, we study the case when the sequence collapses, which may occur when dilating about infinite time singularities. In this case we classify the possible Gromov-Hausdorff limits and construct 2-dimensional virtual limits. The virtual limits are constructed using Fukaya theory of the limits of local covers. We then show that the virtual limit arising from appropriate dilations of a Type IIb singularity is always Hamilton's cigar soliton solution.Comment: 28 page

Seed for general rotating non-extremal black holes of N=8 supergravity

We describe the most general asymptotically flat, stationary, non-extremal, dyonic black hole of the four-dimensional N = 2 supergravity coupled to 3 vector multiplets that describes the low-energy regime of the STU model. Under U-dualities, this can be used as a seed to generate all single-centered stationary black holes of N = 8 supergravity. The independent conserved charges are the mass, angular momentum, four electric charges and four magnetic charges; an independent NUT charge can also be added. Several aspects of the black hole are presented, including thermodynamics, the BPS limit, the near-horizon limit in the extremal fast and slow rotating cases, properties of black hole horizons, the existence of Killing tensors and the separability of probe scalars.Comment: BPS limit, extremal fast and slow rotating branches discussed. 1 Mathematica file of solution. Published versio