The Gregory-Laflamme instability for the D2-D0 bound state

The D2-D0 bound state exhibits a Gregory-Laflamme instability when it is sufficiently non-extremal. If there are no D0-branes, the requisite non-extremality is finite. When most of the extremal mass comes from D0-branes, the requisite non-extremality is very small. The location of the threshhold for the instability is determined using a local thermodynamic analysis which is then checked against a numerical analysis of the linearized equations of motion. The thermodynamic analysis reveals an instability of non-commutative field theory at finite temperature, which may occur only at very long wavelengths as the decoupling limit is approached.Comment: 19 pages, Latex2e. v2: two refs added. v3: clearer exposition in section

The First Law for Boosted Kaluza-Klein Black Holes

We study the thermodynamics of Kaluza-Klein black holes with momentum along the compact dimension, but vanishing angular momentum. These black holes are stationary, but non-rotating. We derive the first law for these spacetimes and find that the parameter conjugate to variations in the length of the compact direction is an effective tension, which generally differs from the ADM tension. For the boosted black string, this effective tension is always positive, while the ADM tension is negative for large boost parameter. We also derive two Smarr formulas, one that follows from time translation invariance, and a second one that holds only in the case of exact translation symmetry in the compact dimension. Finally, we show that the `tension first law' derived by Traschen and Fox in the static case has the form of a thermodynamic Gibbs-Duhem relation and give its extension in the stationary, non-rotating case.Comment: 20 pages, 0 figures; v2 - reference adde

Small Black Holes on Cylinders

We find the metric of small black holes on cylinders, i.e. neutral and static black holes with a small mass in d-dimensional Minkowski-space times a circle. The metric is found using an ansatz for black holes on cylinders proposed in hep-th/0204047. We use the new metric to compute corrections to the thermodynamics which is seen to deviate from that of the (d+1)-dimensional Schwarzschild black hole. Moreover, we compute the leading correction to the relative binding energy which is found to be non-zero. We discuss the consequences of these results for the general understanding of black holes and we connect the results to the phase structure of black holes and strings on cylinders.Comment: 23 pages, 1 figure. v2: typos corrected, introduction expanded, v3: presentation of sections 2 and 3 reordered and improved, explanatory remarks added, refs adde

The Phase Structure of Higher-Dimensional Black Rings and Black Holes

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 x 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 ultra-spinning 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.Comment: 61 pages, 6 figures, latex. v2: Added refs., typos corrected, improved section 8. v3: minor changes, version appearing in JHE

Uniqueness Theorem for Black Hole Space-Times with Multiple Disconnected Horizons

We show uniqueness of stationary and asymptotically flat black hole space-times with multiple disconnected horizons and with two rotational Killing vector fields in the context of five-dimensional minimal supergravity (Einstein-Maxwell-Chern-Simons gravity). The novelty in this work is the introduction in the uniqueness theorem of intrinsic local charges measured near each horizon as well as the measurement of local fluxes besides the asymptotic charges that characterize a particular solution. A systematic method of defining the boundary conditions on the fields that specify a black hole space-time is given based on the study of its rod structure (domain structure). Also, an analysis of known solutions with disconnected horizons is carried out as an example of an application of this theorem.Comment: 28 pages, 5 figures. v3: Further improvements on uniqueness theorem, Lemma introduced for clarity of derivation, new quantities introduced to treat special case with zero flux, refs. added, typos fixe

Formation of Five-Dimensional String Solutions from the Gravitational Collapse

We study the formation of five-dimensional string solutions including the Gregory-Laflamme (GL) black string, the Kaluza-Klein (KK) bubble, and the geometry with a naked singularity from the gravitational collapse. The interior solutions of five-dimensional Einstein equations describe collapsing non-isotropic matter clouds. It is shown that the matter cloud always forms the GL black string solution while the KK bubble solution cannot be formed. The numerical study seems to suggest that the collapsing matter forms the geometries with timelike naked curvature singularities, which should be taken cautiously as the general relativity is not reliable in the strong curvature regime.Comment: 17 pages, 10 figures, LaTeX, to appear in Class. Quant. Grav., a appendix and some discussions added, title change

Thermodynamics of Squashed Kaluza-Klein Black Holes and Black Strings -- A Comparison of Reference Backgrounds --

We investigate thermodynamics constructed on different background reference spacetimes for squashed Kaluza-Klein (SqKK) black hole and electrically charged black string in five-dimensional Einstein-Maxwell system. Two spacetimes are possible to be reference spacetimes giving finite gravitational classical actions: one is four-dimensional Minkowski times a circle and the other is the KK monopole. The boundary of the SqKK black hole can not be matched perfectly to that of the former reference spacetime because of the difference in topology. However, the resultant classical action coincides with that calculated by the counterterm subtraction scheme. The boundary of the KK monopole has the same topology with that of the SqKK black hole and can be matched to the boundary of the black hole perfectly. The resultant action takes different value from the result given by using the former reference spacetime. After a brief review of thermodynamic quantities of the black hole solutions, we calculate thermodynamic potentials relevant for several thermodynamic environments. The most stable state is different for each environment: For example, the KK monopole is the most stable state in isothermal environment with fixed gravitational tension. On the other hand, when the size of the extra-dimension is fixed, the Minkowski times a circle is the most stable. It is shown that these two spacetimes can be reference spacetimes of the five-dimensional black string.Comment: 28 pages; references added, typo corrected;version accepted for publication in Class. Quantum Gra

New Penrose Limits and AdS/CFT

We find a new Penrose limit of AdS_5 x S^5 giving the maximally supersymmetric pp-wave background with two explicit space-like isometries. This is an important missing piece in studying the AdS/CFT correspondence in certain subsectors. In particular whereas the Penrose limit giving one space-like isometry is useful for the SU(2) sector of N=4 SYM, this new Penrose limit is instead useful for studying the SU(2|3) and SU(1,2|3) sectors. In addition to the new Penrose limit of AdS_5 x S^5 we also find a new Penrose limit of AdS_4 x CP^3.Comment: 30 page

Matched Asymptotic Expansion for Caged Black Holes - Regularization of the Post-Newtonian Order

The "dialogue of multipoles" matched asymptotic expansion for small black holes in the presence of compact dimensions is extended to the Post-Newtonian order for arbitrary dimensions. Divergences are identified and are regularized through the matching constants, a method valid to all orders and known as Hadamard's partie finie. It is closely related to "subtraction of self-interaction" and shows similarities with the regularization of quantum field theories. The black hole's mass and tension (and the "black hole Archimedes effect") are obtained explicitly at this order, and a Newtonian derivation for the leading term in the tension is demonstrated. Implications for the phase diagram are analyzed, finding agreement with numerical results and extrapolation shows hints for Sorkin's critical dimension - a dimension where the transition turns second order.Comment: 28 pages, 5 figures. v2:published versio