Scalar field in a minimally coupled brane world: no-hair and other no-go theorems

In the brane-world framework, we consider static, spherically symmetric configurations of a scalar field with the Lagrangian (\d\phi)^2/2 - V(\phi), confined on the brane. We use the 4D Einstein equations on the brane obtained by Shiromizu et al., containing the usual stress tensor T\mN, the tensor \Pi\mN, quadratic in T\mN, and E\mN describing interaction with the bulk. For models under study, the tensor \Pi\mN has zero divergence, so we can consider a "minimally coupled" brane with E\mN = 0, whose 4D gravity is decoupled from the bulk geometry. Assuming E\mN =0, we try to extend to brane worlds some theorems valid for scalar fields in general relativity (GR). Thus, the list of possible global causal structures in all models under consideration is shown to be the same as is known for vacuum with a $Lambda$ term in GR: Minkowski, Schwarzschild, (A)dS and Schwarzschild-(A)dS. A no-hair theorem, saying that, given a potential $V\geq 0$, asymptotically flat black holes cannot have nontrivial external scalar fields, is proved under certain restrictions. Some objects, forbidden in GR, are allowed on the brane, e.g, traversable wormholes supported by a scalar field, but only at the expense of enormous matter densities in the strong field region.Comment: 8 pages, Latex2e. Numerical estimates and a few references adde

Wavelet-function formation in the problem of music signal identification

Approach allowing forming wavelet-functions on the basis of periodic signals and signal fragments of musical instruments has been suggested. The required and sufficient conditions made to the formed wavelet-functions were considered. The experiment allowing identifying some harmonic components of a signal localized in time was described. The possibility of applying the developed approach in the tasks of identifying complex musical signals was show

A Note on the Cosmological Dynamics in Finite-Range Gravity

In this note we consider the homogeneous and isotropic cosmology in the finite-range gravity theory recently proposed by Babak and Grishchuk. In this scenario the universe undergoes late time accelerated expansion if both the massive gravitons present in the model are tachyons. We carry out the phase space analysis of the system and show that the late-time acceleration is an attractor of the model.Comment: RevTex, 4 pages, two figures, New references added, To appear in IJMP

Efficient numerical diagonalization of hermitian 3x3 matrices

A very common problem in science is the numerical diagonalization of symmetric or hermitian 3x3 matrices. Since standard "black box" packages may be too inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with an analytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. The analytical algorithm outperforms the others by more than a factor of 2, but becomes inaccurate or may even fail completely if the matrix entries differ greatly in magnitude. This can mostly be circumvented by using a hybrid method, which falls back to QL if conditions are such that the analytical calculation might become too inaccurate. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from http://www.mpi-hd.mpg.de/~globes/3x3/ .Comment: 13 pages, no figures, new hybrid algorithm added, matches published version, typo in Eq. (39) corrected; software library available at http://www.mpi-hd.mpg.de/~globes/3x3

A symplectic realization of the Volterra lattice

We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational Volterra bracket is obtained using a negative recursion operator.Comment: 8 page