On Black-Brane Instability In an Arbitrary Dimension

The black-hole black-string system is known to exhibit critical dimensions and therefore it is interesting to vary the spacetime dimension $D$, treating it as a parameter of the system. We derive the large $D$ asymptotics of the critical, i.e. marginally stable, string following an earlier numerical analysis. For a background with an arbitrary compactification manifold we give an expression for the critical mass of a corresponding black brane. This expression is completely explicit for ${\bf T}^n$, the $n$ dimensional torus of an arbitrary shape. An indication is given that by employing a higher dimensional torus, rather than a single compact dimension, the total critical dimension above which the nature of the black-brane black-hole phase transition changes from sudden to smooth could be as low as $D\leq 11$.Comment: 1+14 pages, 2 eps figures. Replaced with the published versio

From Black Strings to Black Holes

Using recently developed numerical methods, we examine neutral compactified non-uniform black strings which connect to the Gregory-Laflamme critical point. By studying the geometry of the horizon we give evidence that this branch of solutions may connect to the black hole solutions, as conjectured by Kol. We find the geometry of the topology changing solution is likely to be nakedly singular at the point where the horizon radius is zero. We show that these solutions can all be expressed in the coordinate system discussed by Harmark and Obers.Comment: 6 pages, 5 figures, RevTe

Static Axisymmetric Vacuum Solutions and Non-Uniform Black Strings

We describe new numerical methods to solve the static axisymmetric vacuum Einstein equations in more than four dimensions. As an illustration, we study the compactified non-uniform black string phase connected to the uniform strings at the Gregory-Laflamme critical point. We compute solutions with a ratio of maximum to minimum horizon radius up to nine. For a fixed compactification radius, the mass of these solutions is larger than the mass of the classically unstable uniform strings. Thus they cannot be the end state of the instability.Comment: 48 pages, 13 colour figures; v2: references correcte

Holographic repulsion and confinement in gauge theory

We show that for asymptotically anti-deSitter backgrounds with negative energy, such as the AdS soliton and regulated negative mass AdS-Schwarzshild metrics, the Wilson loop expectation value in the AdS/CFT conjecture exhibits a Coulomb to confinement transition. We also show that the quark-antiquark ($q \bar q$) potential can be interpreted as affine time along null geodesics on the minimal string world sheet,and that its intrinsic curvature provides a signature of transition to confinement phase. The result demonstrates a UV/IR relation in that the boundary separation of the $q \bar{q}$ pair exhibits an inverse relationship with the radial descent of the world sheet into the bulk. Our results suggest a generic (holographic) relationship between confinement in gauge theory and repulsive gravity, which in turn is connected with singularity avoidance in quantum gravity.Comment: 8 pages, 4 figure

Classical Effective Field Theory for Weak Ultra Relativistic Scattering

Inspired by the problem of Planckian scattering we describe a classical effective field theory for weak ultra relativistic scattering in which field propagation is instantaneous and transverse and the particles' equations of motion localize to the instant of passing. An analogy with the non-relativistic (post-Newtonian) approximation is stressed. The small parameter is identified and power counting rules are established. The theory is applied to reproduce the leading scattering angle for either a scalar interaction field or electro-magnetic or gravitational; to compute some subleading corrections, including the interaction duration; and to allow for non-zero masses. For the gravitational case we present an appropriate decomposition of the gravitational field onto the transverse plane together with its whole non-linear action. On the way we touch upon the relation with the eikonal approximation, some evidence for censorship of quantum gravity, and an algebraic ring structure on 2d Minkowski spacetime.Comment: 29 pages, 2 figures. v4: Duration of interaction is determined in Sec 4 and detailed in App C. Version accepted for publication in JHE

Diffusion limited aggregation as a Markovian process: site-sticking conditions

Cylindrical lattice diffusion limited aggregation (DLA), with a narrow width N, is solved for site-sticking conditions using a Markovian matrix method (which was previously developed for the bond-sticking case). This matrix contains the probabilities that the front moves from one configuration to another at each growth step, calculated exactly by solving the Laplace equation and using the proper normalization. The method is applied for a series of approximations, which include only a finite number of rows near the front. The fractal dimensionality of the aggregate is extrapolated to a value near 1.68.Comment: 27 Revtex pages, 16 figure

Non-Relativistic Gravitation: From Newton to Einstein and Back

We present an improvement to the Classical Effective Theory approach to the non-relativistic or Post-Newtonian approximation of General Relativity. The "potential metric field" is decomposed through a temporal Kaluza-Klein ansatz into three NRG-fields: a scalar identified with the Newtonian potential, a 3-vector corresponding to the gravito-magnetic vector potential and a 3-tensor. The derivation of the Einstein-Infeld-Hoffmann Lagrangian simplifies such that each term corresponds to a single Feynman diagram providing a clear physical interpretation. Spin interactions are dominated by the exchange of the gravito-magnetic field. Leading correction diagrams corresponding to the 3PN correction to the spin-spin interaction and the 2.5PN correction to the spin-orbit interaction are presented.Comment: 10 pages, 3 figures. v2: published version. v3: Added a computation of Einstein-Infeld-Hoffmann in higher dimensions within our improved ClEFT which partially confirms and partially corrects a previous computation. See notes added at end of introductio

E(7) Symmetric Area of the Black Hole Horizon

Extreme black holes with 1/8 of unbroken N=8 supersymmetry are characterized by the non-vanishing area of the horizon. The central charge matrix has four generic eigenvalues. The area is proportional to the square root of the invariant quartic form of $E_{7(7)}$. It vanishes in all cases when 1/4 or 1/2 of supersymmetry is unbroken. The supergravity non-renormalization theorem for the area of the horizon in N=8 case protects the unique U-duality invariant.Comment: a reference added, misprints remove

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

Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics

We show that under variation of moduli fields $\phi$ the first law of black hole thermodynamics becomes $dM = {\kappa dA\over 8\pi} + \Omega dJ + \psi dq + \chi dp - \Sigma d\phi$, where $\Sigma$ are the scalar charges. We also show that the ADM mass is extremized at fixed $A$, $J$, $(p,q)$ when the moduli fields take the fixed value $\phi_{\rm fix}(p,q)$ which depend only on electric and magnetic charges. It follows that the least mass of any black hole with fixed conserved electric and magnetic charges is given by the mass of the double-extreme black hole with these charges. Our work allows us to interpret the previously established result that for all extreme black holes the moduli fields at the horizon take a value $\phi= \phi_{\rm fix}(p,q)$ depending only on the electric and magnetic conserved charges: $\phi_{\rm fix}(p,q)$ is such that the scalar charges $\Sigma ( \phi_{\rm fix}, (p,q))=0$.Comment: 3 pages, no figures, more detailed versio