Thermodynamics of Spinning Branes and their Dual Field Theories

We present a general analysis of the thermodynamics of spinning black p-branes of string and M-theory. This is carried out both for the asymptotically-flat and near-horizon case, with emphasis on the latter. In particular, we use the conjectured correspondence between the near-horizon brane solutions and field theories with 16 supercharges in various dimensions to describe the thermodynamic behavior of these field theories in the presence of voltages under the R-symmetry. Boundaries of stability are computed for all spinning branes both in the grand canonical and canonical ensemble, and the effect of multiple angular momenta is considered. A recently proposed regularization of the field theory is used to compute the corresponding boundaries of stability at weak coupling. For the D2, D3, D4, M2 and M5-branes the critical values of Omega/T in the weak and strong coupling limit are remarkably close. Finally, we also show that for the spinning D3-brane the tree level R^4 correction supports the conjecture of a smooth interpolating function between the free energy at weak and strong coupling.Comment: 59 pages, JHEP class. Minor typos corrected, added remark on positivity of temperature, Sec. 6.1 improved, references adde

Phase Structure of Non-Commutative Field Theories and Spinning Brane Bound States

General spinning brane bound states are constructed, along with their near-horizon limits which are relevant as dual descriptions of non-commutative field theories. For the spinning D-brane world volume theories with a B-field a general analysis of the gauge coupling phase structure is given, exhibiting various novel features, already at the level of zero angular momenta. We show that the thermodynamics is equivalent to the commutative case at large N and we discuss the possibility and consequences of finite N. As an application of the general analysis, the range of validity of the thermodynamics for the NCSYM is discussed. In view of the recently conjectured existence of a 7-dimensional NCSYM, the thermodynamics of the spinning D6-brane theory, for which a stable region can be found, is presented in detail. Corresponding results for the spinning M5-M2 brane bound state, including the near-horizon limit and thermodynamics, are given as well.Comment: 34 pages, JHEP class. minor corrections, final JHEP versio

Phases of Kaluza-Klein Black Holes: A Brief Review

We review the latest progress in understanding the phase structure of static and neutral Kaluza-Klein black holes, i.e. static and neutral solutions of pure gravity with an event horizon that asymptote to a d-dimensional Minkowski-space times a circle. We start by reviewing the (mu,n) phase diagram and the split-up of the phase structure into solutions with an internal SO(d-1) symmetry and solutions with Kaluza-Klein bubbles. We then discuss the uniform black string, non-uniform black string and localized black hole phases, and how those three phases are connected, involving issues such as classical instability and horizon-topology changing transitions. Finally, we review the bubble-black hole sequences, their place in the phase structure and interesting aspects such as the continuously infinite non-uniqueness of solutions for a given mass and relative tension.Comment: 23 pages, 5 figures. v2: Typo fixe

New Phase Diagram for Black Holes and Strings on Cylinders

We introduce a novel type of phase diagram for black holes and black strings on cylinders. The phase diagram involves a new asymptotic quantity called the relative binding energy. We plot the uniform string and the non-uniform string solutions in this new phase diagram using data of Wiseman. Intersection rules for branches of solutions in the phase diagram are deduced from a new Smarr formula that we derive.Comment: 19 pages, 6 figures, v2: typos corrected, v3: refs. added, comment on bounds on the relative binding energy n added in end of section

Analytic Evidence for Continuous Self Similarity of the Critical Merger Solution

The double cone, a cone over a product of a pair of spheres, is known to play a role in the black-hole black-string phase diagram, and like all cones it is continuously self similar (CSS). Its zero modes spectrum (in a certain sector) is determined in detail, and it implies that the double cone is a co-dimension 1 attractor in the space of those perturbations which are smooth at the tip. This is interpreted as strong evidence for the double cone being the critical merger solution. For the non-symmetry-breaking perturbations we proceed to perform a fully non-linear analysis of the dynamical system. The scaling symmetry is used to reduce the dynamical system from a 3d phase space to 2d, and obtain the qualitative form of the phase space, including a non-perturbative confirmation of the existence of the "smoothed cone".Comment: 25 pages, 4 figure

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

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