Solution of the dispersionless Hirota equations

The dispersionless differential Fay identity is shown to be equivalent to a kernel expansion providing a universal algebraic characterization and solution of the dispersionless Hirota equations. Some calculations based on D-bar data of the action are also indicated.Comment: Late

On the water-bag model of dispersionless KP hierarchy

We investigate the bi-Hamiltonian structure of the waterbag model of dKP for two component case. One can establish the third-order and first-order Hamiltonian operator associated with the waterbag model. Also, the dispersive corrections are discussed.Comment: 19 page

Coisotropic deformations of associative algebras and dispersionless integrable hierarchies

The paper is an inquiry of the algebraic foundations of the theory of dispersionless integrable hierarchies, like the dispersionless KP and modified KP hierarchies and the universal Whitham's hierarchy of genus zero. It stands out for the idea of interpreting these hierarchies as equations of coisotropic deformations for the structure constants of certain associative algebras. It discusses the link between the structure constants and the Hirota's tau function, and shows that the dispersionless Hirota's bilinear equations are, within this approach, a way of writing the associativity conditions for the structure constants in terms of the tau function. It also suggests a simple interpretation of the algebro-geometric construction of the universal Whitham's equations of genus zero due to Krichever.Comment: minor misprints correcte

Perturbations of Gauss-Bonnet Black Strings in Codimension-2 Braneworlds

We derive the Lichnerowicz equation in the presence of the Gauss-Bonnet term. Using the modified Lichnerowicz equation we study the metric perturbations of Gauss-Bonnet black strings in Codimension-2 Braneworlds.Comment: 26 pages, no figures, clarifying comments and one reference added, to be published in JHE

Geometry and cosmological perturbations in the bulk inflaton model

We consider a braneworld inflation model driven by the dynamics of a scalar field living in the 5-dimensional bulk, the so-called ``bulk inflaton model'', and investigate the geometry in the bulk and large scale cosmological perturbations on the brane. The bulk gravitational effects on the brane are described by a projection of the 5-dimensional Weyl tensor, which we denote by $E_{\mu\nu}$. Focusing on a tachionic potential model, we take a perturbative approach in the anti-de Sitter (AdS$_5$) background with a single de Sitter brane. We first formulate the evolution equations for $E_{\mu\nu}$ in the bulk. Next, applying them to the case of a spatially homogeneous brane, we obtain two different integral expressions for $E_{\mu\nu}$. One of them reduces to the expression obtained previously when evaluated on the brane. The other is a new expression that may be useful for analyzing the bulk geometry. Then we consider superhorizon scale cosmological perturbations and evaluate the bulk effects onto the brane. In the limit $H^2\ell^2\ll1$, where $H$ is the Hubble parameter on the brane and $\ell$ is the bulk curvature radius, we find that the effective theory on the brane is identical to the 4-dimensional Einstein-scalar theory with a simple rescaling of the potential even under the presence of inhomogeneities. % atleast on super-Hubble horizon scales. In particular, it is found that the anticipated non-trivial bulk effect due to the spatially anisotropic part of $E_{\mu\nu}$ may appear only at %second order in the low energy expansion, i.e., at $O(H^4\ell^4)$.Comment: 21 pages including 6 pages for several appendixes, no figure

Supersymmetric Intersecting Branes on the Waves

We construct a general family of supersymmetric solutions in time- and space-dependent wave backgrounds in general supergravity theories describing single and intersecting p-branes embedded into time-dependent dilaton-gravity plane waves of an arbitrary (isotropic) profile, with the brane world-volume aligned parallel to the propagation direction of the wave. We discuss how many degrees of freedom we have in the solutions. We also propose that these solutions can be used to describe higher-dimensional time-dependent "black holes", and discuss their property briefly.Comment: 12 pages, LaTe

S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies

We introduce an S-function formulation for the recently found r-th dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also a connection of these $S$-functions with the Orlov functions of the hierarchies. Then, we discuss a reduction scheme for the hierarchies that together with the $S$-function formulation leads to hodograph systems for the associated solutions. We consider also the connection of these reductions with those of the dispersionless KP hierarchy and with hydrodynamic type systems. In particular, for the 1-component and 2-component reduction we derive, for both hierarchies, ample sets of examples of explicit solutions.Comment: 35 pages, uses AMS-Latex, Hyperref, Geometry, Array and Babel package

Small localized black holes in a braneworld: Formulation and numerical method

No realistic black holes localized on a 3-brane in the Randall-Sundrum infinite braneworld have been found so far. The problem of finding a static black hole solution is reduced to a boundary value problem. We solve it by means of a numerical method, and show numerical examples of a localized black hole whose horizon radius is small compared to the bulk curvature scale. The sequence of small localized black holes exhibits a smooth transition from a five-dimensional Schwarzschild black hole, which is a solution in the limit of small horizon radius. The localized black hole tends to flatten as its horizon radius increases. However, it becomes difficult to find black hole solutions as its horizon radius increases.Comment: RevTeX, 13 pages, 6 figures, references corrected, typos corrected; to appear in Phys.Rev.

On Brane World Cosmological Perturbations

We discuss the scalar cosmological perturbations in a 3-brane world with a 5D bulk. We first show explicitly how the effective perturbed Einstein's equations on the brane (involving the Weyl fluid) are encoded into Mukohyama's master equation. We give the relation between Mukohyama's master variable and the perturbations of the Weyl fluid, we also discuss the relation between the former and the perturbations of matter and induced metric on the brane. We show that one can obtain a boundary condition on the brane for the master equation solely expressible in term of the master variable, in the case of a perfect fluid with adiabatic perturbations on a Randall-Sundrum (RS) or Dvali-Gabadadze-Porrati (DGP) brane. This provides an easy way to solve numerically for the evolution of the perturbations as well as should shed light on the various approximations done in the literature to deal with the Weyl degrees of freedom.Comment: 36 pages, 1 figur

Measurement of the Inclusive Semi-electronic D0D^0 Branching Fraction

Using the angular correlation between the $\pi^+$ emitted in a $D^{*+} \rightarrow D^0 \pi^+$ decay and the $e^+$ emitted in the subsequent $D^0 \rightarrow Xe^+\nu$ decay, we have measured the branching fraction for the inclusive semi-electronic decay of the $D^0$ meson to be: {\cal B}(D^0 \rightarrow X e^+ \nu) = [6.64 \pm 0.18 (stat.) \pm 0.29 (syst.)] \%. The result is based on 1.7 fb$^{-1}$ of $e^+e^-$ collisions recorded by the CLEO II detector located at the Cornell Electron Storage Ring (CESR). Combining the analysis presented in this paper with previous CLEO results we find, \frac{{\cal B} (D^0 \rightarrow X e^+ \nu)} {{\cal B} (D^0 \rightarrow K^- \pi^+)} = 1.684 \pm 0.056 (stat.) \pm 0.093(syst.) and \frac{{\cal B}(D\rightarrow K^-e^+\nu)} {{\cal B}(D\rightarrow Xe^+\nu)} = 0.581 \pm 0.023 (stat.) \pm 0.028(syst.). The difference between the inclusive rate and the sum of the measured exclusive branching fractions (measured at CLEO and other experiments) is $(3.3 \pm 7.2) \%$ of the inclusive rate.Comment: Latex file, 33pages, 4 figures Submitted to PR