A black hole instability in five dimensions?

We study the moduli-space scattering of a two-charge supertube in the background of a rotating BPS D1-D5-P black hole in 4+1 dimensions, extending the static analysis of Bena and Kraus (hep-th/0402144). While the magnetic forces associated with this motion change the details considerably, the final conclusion is similar to that of the static analysis: we find that one can bring the supertube to the horizon, so that the BMPV black hole and the supertube merge. However, our analysis shows that this can occur even at significantly larger values of the angular momentum than was indicated by the static analysis. For a range of parameters, conservation laws and the area theorem forbid the result of the merger from being any single known object: neither near-extremal black holes nor non-supersymmetric black rings are allowed. Such results suggest that the merger triggers an instability of the rotating D1-D5-P black hole, perhaps leading to bifurcation into a pair of black objects.Comment: 25 pages, 4 figures; v2: references adde

Geroch Group Description of Black Holes

On one hand the Geroch group allows one to associate spacetime independent matrices with gravitational configurations that effectively only depend on two coordinates. This class includes stationary axisymmetric four- and five-dimensional black holes. On the other hand, a recently developed inverse scattering method allows one to factorize these matrices to explicitly construct the corresponding spacetime configurations. In this work we demonstrate the construction as well as the factorization of Geroch group matrices for a wide class of black hole examples. In particular, we obtain the Geroch group SL(3,R) matrices for the five-dimensional Myers-Perry and Kaluza-Klein black holes and the Geroch group SU(2,1) matrix for the four-dimensional Kerr-Newman black hole. We also present certain non-trivial relations between the Geroch group matrices and charge matrices for these black holes.Comment: 29 pages, no figures; v2: references added; v3: minor changes, matches published versio

Extremal limits of the Cvetic-Youm black hole and nilpotent orbits of G2(2)

We study extremal cohomogeneity one five-dimensional asymptotically flat black holes of minimal supergravity in terms of the geodesics generated by nilpotent elements of the Lie algebra g2(2) on the coset manifold G2(2)/SO(2,2). There are two branches of regular extremal black holes with these properties: (i) the supersymmetric BMPV branch, and (ii) the non-supersymmetric extremal branch. We show that both of these branches are reproduced by nilpotent SO(2,2)-orbits. Furthermore, we show that the partial ordering of nilpotent orbits of G2(2) is in one-to-one correspondence with the phase diagram of these extremal black holes.Comment: 17 pages, 2 figures; v2 two minus sign typos in appendix A equation (A.3) corrected, no other change

Asymptotic Flatness, Taub-NUT, and Variational Principle

Using hyperbolic temporal and spatial cut-offs to define 4d asymptotically flat spacetimes, we show that supertranslation ambiguities in the asymptotic fields can all be removed even in the presence of gravitational magnetic charges. We then show that configurations with different electric and magnetic four-momenta can be consistently considered in the Mann-Marolf variational principle. This generalizes the previous result where variations over asymptotically flat configurations with fixed magnetic four-momenta were considered. We also express Kerr Taub-NUT metric to the leading and next to leading order in the Beig-Schmidt form, and compare the asymptotic form with the tensor harmonics on 3d de Sitter space.Comment: 18 pages, no figures; v2 19 pages, minor changes, to appear in Phys Rev

On Asymptotic Flatness and Lorentz Charges

In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence free tensors that we construct from the equations of motion. Second, we show that integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmae on tensor fields on three dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmae.Comment: 26 pages; no figures; v2: minor changes; v3: clarifications + references + a new lemma added, results unaffecte

Inverse Scattering and the Geroch Group

We study the integrability of gravity-matter systems in D=2 spatial dimensions with matter related to a symmetric space G/K using the well-known linear systems of Belinski-Zakharov (BZ) and Breitenlohner-Maison (BM). The linear system of BM makes the group structure of the Geroch group manifest and we analyse the relation of this group structure to the inverse scattering method of the BZ approach in general. Concrete solution generating methods are exhibited in the BM approach in the so-called soliton transformation sector where the analysis becomes purely algebraic. As a novel example we construct the Kerr-NUT solution by solving the appropriate purely algebraic Riemann-Hilbert problem in the BM approach.Comment: 30 pages. v2: Typos correcte

Holographic description of non-supersymmetric orbifolded D1-D5-P solutions

Non-supersymmetric black hole microstates are of great interest in the context of the black hole information paradox. We identify the holographic description of the general class of non-supersymmetric orbifolded D1-D5-P supergravity solutions found by Jejjala, Madden, Ross and Titchener. This class includes both completely smooth solutions and solutions with conical defects, and in the near-decoupling limit these solutions describe degrees of freedom in the cap region. The CFT description involves a general class of states obtained by fractional spectral flow in both left-moving and right-moving sectors, generalizing previous work which studied special cases in this class. We compute the massless scalar emission spectrum and emission rates in both gravity and CFT and find perfect agreement, thereby providing strong evidence for our proposed identification. We also investigate the physics of ergoregion emission as pair creation for these orbifolded solutions. Our results represent the largest class of non-supersymmetric black hole microstate geometries with identified CFT duals presently known.Comment: 35 pages, v2: comments added, typos corrected, reference adde